Internet Engineering Task Force (IETF) G. Enyedi
Request for Comments: 7811 A. Csaszar
Category: Standards Track Ericsson
ISSN: 20701721 A. Atlas
C. Bowers
Juniper Networks
A. Gopalan
University of Arizona
June 2016
An Algorithm for Computing IP/LDP Fast Reroute
Using Maximally Redundant Trees (MRTFRR)
Abstract
This document supports the solution put forth in "An Architecture for
IP/LDP Fast Reroute Using Maximally Redundant Trees (MRTFRR)"
(RFC 7812) by defining the associated MRT Lowpoint algorithm that is
used in the Default MRT Profile to compute both the necessary
Maximally Redundant Trees with their associated next hops and the
alternates to select for MRTFRR.
Status of This Memo
This is an Internet Standards Track document.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Further information on
Internet Standards is available in Section 2 of RFC 7841.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
http://www.rfceditor.org/info/rfc7811.
Copyright Notice
Copyright (c) 2016 IETF Trust and the persons identified as the
document authors. All rights reserved.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Requirements Language . . . . . . . . . . . . . . . . . . . . 5
3. Terminology and Definitions . . . . . . . . . . . . . . . . . 5
4. Algorithm Key Concepts . . . . . . . . . . . . . . . . . . . 6
4.1. Partial Ordering for Disjoint Paths . . . . . . . . . . . 7
4.2. Finding an Ear and the Correct Direction . . . . . . . . 8
4.3. Lowpoint Values and Their Uses . . . . . . . . . . . . . 11
4.4. Blocks in a Graph . . . . . . . . . . . . . . . . . . . . 14
4.5. Determining Localroot and Assigning BlockID . . . . . . 16
5. MRT Lowpoint Algorithm Specification . . . . . . . . . . . . 18
5.1. Interface Ordering . . . . . . . . . . . . . . . . . . . 18
5.2. MRT Island Identification . . . . . . . . . . . . . . . . 21
5.3. GADAG Root Selection . . . . . . . . . . . . . . . . . . 21
5.4. Initialization . . . . . . . . . . . . . . . . . . . . . 22
5.5. Constructing the GADAG Using Lowpoint Inheritance . . . . 23
5.6. Augmenting the GADAG by Directing All Links . . . . . . . 25
5.7. Compute MRT Next Hops . . . . . . . . . . . . . . . . . . 29
5.7.1. MRT Next Hops to All Nodes Ordered with Respect to
the Computing Node . . . . . . . . . . . . . . . . . 29
5.7.2. MRT Next Hops to All Nodes Not Ordered with Respect
to the Computing Node . . . . . . . . . . . . . . . . 30
5.7.3. Computing Redundant Tree Next Hops in a 2Connected
Graph . . . . . . . . . . . . . . . . . . . . . . . . 31
5.7.4. Generalizing for a Graph That Isn't 2Connected . . . 33
5.7.5. Complete Algorithm to Compute MRT Next Hops . . . . . 34
5.8. Identify MRT Alternates . . . . . . . . . . . . . . . . . 36
5.9. Named ProxyNodes . . . . . . . . . . . . . . . . . . . . 44
5.9.1. Determining ProxyNode Attachment Routers . . . . . . 45
5.9.2. Computing If an Island Neighbor (IN) Is LoopFree . . 45
5.9.3. Computing MRT Next Hops for ProxyNodes . . . . . . . 47
5.9.4. Computing MRT Alternates for ProxyNodes . . . . . . 53
6. MRT Lowpoint Algorithm: NextHop Conformance . . . . . . . . 61
7. Broadcast Interfaces . . . . . . . . . . . . . . . . . . . . 61
7.1. Computing MRT Next Hops on Broadcast Networks . . . . . . 62
7.2. Using MRT Next Hops as Alternates in the Event of
Failures on Broadcast Networks . . . . . . . . . . . . . 63
8. Evaluation of Alternative Methods for Constructing GADAGs . . 64
9. Operational Considerations . . . . . . . . . . . . . . . . . 66
9.1. GADAG Root Selection . . . . . . . . . . . . . . . . . . 67
9.2. DestinationRooted GADAGs . . . . . . . . . . . . . . . . 67
10. Security Considerations . . . . . . . . . . . . . . . . . . . 67
11. References . . . . . . . . . . . . . . . . . . . . . . . . . 68
11.1. Normative References . . . . . . . . . . . . . . . . . . 68
11.2. Informative References . . . . . . . . . . . . . . . . . 68
Appendix A. Python Implementation of MRT Lowpoint Algorithm . . 70
Appendix B. Constructing a GADAG Using SPFs . . . . . . . . . . 110
Appendix C. Constructing a GADAG Using a Hybrid Method . . . . . 115
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 117
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 118
1. Introduction
MRT Fast Reroute requires that packets can be forwarded not only on
the shortestpath tree, but also on two Maximally Redundant Trees
(MRTs), referred to as the MRTBlue and the MRTRed. A router that
experiences a local failure must also have predetermined which
alternate to use. This document defines how to compute these three
things for use in MRTFRR and describes the algorithm design
decisions and rationale. The algorithm is based on those presented
in [MRTLinear] and expanded in [EnyediThesis]. The MRT Lowpoint
algorithm is required for implementation when the Default MRT Profile
is implemented.
The MRT Lowpoint Algorithm defined in this document, when used for
MRT FastReroute as described in [RFC7812], guarantees 100% recovery
for single failures when the network is 2connected. This guaranteed
coverage does not depend on the link metrics, which an operator may
be using to trafficengineer the IP network. Thus, the link metrics
and general network topology are largely decoupled from the
guaranteed coverage.
Just as packets routed on a hopbyhop basis require that each router
compute a shortestpath tree that is consistent, it is necessary for
each router to compute the MRTBlue next hops and MRTRed next hops
in a consistent fashion. This document defines the MRT Lowpoint
algorithm to be used as a standard in the Default MRT Profile for
MRTFRR.
A router's Forwarding Information Base (FIB) will continue to contain
primary next hops for the current shortestpath tree for forwarding
traffic. In addition, a router's FIB will contain primary next hops
for the MRTBlue for forwarding received traffic on the MRTBlue and
primary next hops for the MRTRed for forwarding received traffic on
the MRTRed.
What alternate next hops a Point of Local Repair (PLR) selects need
not be consistent  but loops must be prevented. To reduce
congestion, it is possible for multiple alternate next hops to be
selected; in the context of MRT alternates, each of those alternate
next hops would be equalcost paths.
This document defines an algorithm for selecting an appropriate MRT
alternate for consideration. Other alternates, e.g., LoopFree
Alternates (LFAs) that are downstream paths, may be preferred when
available. See the "Operational Considerations" section of [RFC7812]
for a more detailed discussion of combining MRT alternates with those
produced by other FRR technologies.
[E][D] [E]<[D]< [E]>[D]
    ^   
   V   V V
[R] [F] [C] [R] [F] [C] [R] [F] [C]
   ^ ^ ^  
      V 
[A][B] [A]>[B] [A]<[B]<
(a) (b) (c)
A 2connected graph MRTBlue towards R MRTRed towards R
Figure 1
The MRT Lowpoint algorithm can handle arbitrary network topologies
where the whole network graph is not 2connected, as in Figure 2, as
well as the easier case where the network graph is 2connected
(Figure 1). Each MRT is a spanning tree. The pair of MRTs provide
two paths from every node X to the root of the MRTs. Those paths
share the minimum number of nodes and the minimum number of links.
Each such shared node is a cutvertex. Any shared links are cut
links.
[E][D] [J]
    
    
[R] [F] [C][G] 
    
    
[A][B] [H]
(a) a graph that is not 2connected
[E]<[D]< [J] [E]>[D] [J]
 ^      ^
V    V V V 
[R] [F] [C]<[G]  [R] [F] [C]<[G] 
^ ^ ^  ^   
   V  V  
[A]>[B] [H] [A]<[B]< [H]
(b) MRTBlue towards R (c) MRTRed towards R
Figure 2: A Network That Is Not 2Connected
2. Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119].
3. Terminology and Definitions
Please see the Terminology section of [RFC7812] for a complete list
of terminology relevant to this document. The list below does not
repeat terminology introduced in that RFC.
spanning tree: A tree that contains links and that connects all
nodes in the network graph.
backedge: In the context of a spanning tree computed via a depth
first search, a backedge is a link that connects a descendant of
a node x with an ancestor of x.
partial ADAG: A subset of an Almost Directed Acyclic Graph (ADAG)
that doesn't yet contain all the nodes in the block. A partial
ADAG is created during the MRT Lowpoint algorithm and then
expanded until all nodes in the block are included and it becomes
an ADAG.
DFS: DepthFirst Search
DFS ancestor: A node n is a DFS ancestor of x if n is on the DFS
tree path from the DFS root to x.
DFS descendant: A node n is a DFS descendant of x if x is on the
DFStree path from the DFS root to n.
ear: A path along nodes that are not yet included in the Generalized
ADAG (GADAG) that starts at a node that is already included in the
GADAG and that ends at a node that is already included in the
GADAG. The starting and ending nodes may be the same node if it
is a cutvertex.
X>>Y or Y<<X: Indicates the relationship between X and Y in a
partial order, such as found in a GADAG. X>>Y means that X is
higher in the partial order than Y. Y<<X means that Y is lower in
the partial order than X.
X>Y or Y<X: Indicates the relationship between X and Y in the total
order, such as found via a topological sort. X>Y means that X is
higher in the total order than Y. Y<X means that Y is lower in
the total order than X.
X ?? Y: Indicates that X is unordered with respect to Y in the
partial order.
UNDIRECTED: In the GADAG, each link is marked as OUTGOING, INCOMING,
or both. Until the directionality of the link is determined, the
link is marked as UNDIRECTED to indicate that its direction hasn't
been determined.
OUTGOING: A link marked as OUTGOING has direction in the GADAG from
the interface's router to the remote end.
INCOMING: A link marked as INCOMING has direction in the GADAG from
the remote end to the interface's router.
4. Algorithm Key Concepts
There are five key concepts that are critical for understanding the
MRT Lowpoint algorithm. The first is the idea of partially ordering
the nodes in a network graph with regard to each other and to the
GADAG root. The second is the idea of finding an ear of nodes and
adding them in the correct direction. The third is the idea of a
Lowpoint value and how it can be used to identify cutvertices and to
find a second path towards the root. The fourth is the idea that a
non2connected graph is made up of blocks, where a block is a
2connected cluster, a cutlink or an isolated node. The fifth is
the idea of a localroot for each node; this is used to compute ADAGs
in each block.
4.1. Partial Ordering for Disjoint Paths
Given any two nodes X and Y in a graph, a particular total order
means that either X<Y or X>Y in that total order. An example would
be a graph where the nodes are ranked based upon their unique IP
loopback addresses. In a partial order, there may be some nodes for
which it can't be determined whether X<<Y or X>>Y. A partial order
can be captured in a directed graph, as shown in Figure 3. In a
graphical representation, a link directed from X to Y indicates that
X is a neighbor of Y in the network graph and X<<Y.
[A]<[R] [E] R << A << B << C << D << E
 ^ R << A << B << F << G << H << D << E
 
V  Unspecified Relationships:
[B]>[C]>[D] C and F
 ^ C and G
  C and H
V 
[F]>[G]>[H]
Figure 3: Directed Graph Showing a Partial Order
To compute MRTs, the root of the MRTs is at both the very bottom and
the very top of the partial ordering. This means that from any node
X, one can pick nodes higher in the order until the root is reached.
Similarly, from any node X, one can pick nodes lower in the order
until the root is reached. For instance, in Figure 4, from G the
higher nodes picked can be traced by following the directed links and
are H, D, E, and R. Similarly, from G the lower nodes picked can be
traced by reversing the directed links and are F, B, A, and R. A
graph that represents this modified partial order is no longer a DAG;
it is termed an Almost DAG (ADAG) because if the links directed to
the root were removed, it would be a DAG.
[A]<[R]<[E] R << A << B << C << R
 ^ ^ R << A << B << C << D << E << R
   R << A << B << F << G << H << D << E << R
V  
[B]>[C]>[D] Unspecified Relationships:
 ^ C and F
  C and G
V  C and H
[F]>[G]>[H]
Figure 4: ADAG Showing a Partial Order with R Lowest and Highest
Most importantly, if a node Y>>X, then Y can only appear on the
increasing path from X to the root and never on the decreasing path.
Similarly, if a node Z<<X, then Z can only appear on the decreasing
path from X to the root and never on the increasing path.
When following the increasing paths, it is possible to pick multiple
higher nodes and still have the certainty that those paths will be
disjoint from the decreasing paths. For example, in the previous
example, node B has multiple possibilities to forward packets along
an increasing path: it can either forward packets to C or F.
4.2. Finding an Ear and the Correct Direction
For simplicity, the basic idea of creating a GADAG by adding ears is
described assuming that the network graph is a single 2connected
cluster so that an ADAG is sufficient. Generalizing to multiple
blocks is done by considering the blockroots instead of the GADAG
root  and the actual algorithm is given in Section 5.5.
In order to understand the basic idea of finding an ADAG, first
suppose that we have already a partial ADAG, which doesn't contain
all the nodes in the block yet, and we want to extend it to cover all
the nodes. Suppose that we find a path from a node X to Y such that
X and Y are already contained by our partial ADAG, but all the
remaining nodes along the path are not added to the ADAG yet. We
refer to such a path as an "ear".
Recall that our ADAG is closely related to a partial order. More
precisely, if we remove root R, the remaining DAG describes a partial
order of the nodes. If we suppose that neither X nor Y is the root,
we may be able to compare them. If one of them is definitely lesser
with respect to our partial order (say X<<Y), we can add the new path
to the ADAG in a direction from X to Y. As an example, consider
Figure 5.
ED E<D E<D<
    ^   ^ 
   V   V  
R F C R F C R F C
    ^   ^ ^
   V   V  
AB A>B A>B
(a) (b) (c)
(a) A 2connected graph
(b) Partial ADAG (C is not included)
(c) Resulting ADAG after adding path (or ear) BCD
Figure 5
In this partial ADAG, node C is not yet included. However, we can
find path BCD, where both endpoints are contained by this partial
ADAG (we say those nodes are "ready" in the following text), and the
remaining node (node C) is not contained yet. If we remove R, the
remaining DAG defines a partial order, and with respect to this
partial order, we can say that B<<D; so, we can add the path to the
ADAG in the direction from B to D (arcs B>C and C>D are added). If
B>>D, we would add the same path in reverse direction.
If, in the partial order where an ear's two ends are X and Y, X<<Y,
then there must already be a directed path from X to Y in the ADAG.
The ear must be added in a direction such that it doesn't create a
cycle; therefore, the ear must go from X to Y.
In the case when X and Y are not ordered with each other, we can
select either direction for the ear. We have no restriction since
neither of the directions can result in a cycle. In the corner case
when one of the endpoints of an ear, say X, is the root (recall that
the two endpoints must be different), we could use both directions
again for the ear because the root can be considered both as smaller
and as greater than Y. However, we strictly pick that direction in
which the root is lower than Y. The logic for this decision is
explained in Section 5.7
A partial ADAG is started by finding a cycle from the root R back to
itself. This can be done by selecting a nonready neighbor N of R
and then finding a path from N to R that doesn't use any links
between R and N. The direction of the cycle can be assigned either
way since it is starting the ordering.
Once a partial ADAG is already present, it will always have a node
that is not the root R in it. The following is a brief proof that a
partial ADAG can always have ears added to it: just select a non
ready neighbor N of a ready node Q, such that Q is not the root R,
find a path from N to the root R in the graph with Q removed. This
path is an ear where the first node of the ear is Q, the next is N,
then the path until the first ready node the path reached (that ready
node is the other endpoint of the path). Since the graph is
2connected, there must be a path from N to R without Q.
It is always possible to select a nonready neighbor N of a ready
node Q so that Q is not the root R. Because the network is
2connected, N must be connected to two different nodes and only one
can be R. Because the initial cycle has already been added to the
ADAG, there are ready nodes that are not R. Since the graph is
2connected, while there are nonready nodes, there must be a non
ready neighbor N of a ready node that is not R.
Generic_Find_Ears_ADAG(root)
Create an empty ADAG. Add root to the ADAG.
Mark root as IN_GADAG.
Select an arbitrary cycle containing root.
Add the arbitrary cycle to the ADAG.
Mark cycle's nodes as IN_GADAG.
Add cycle's nonroot nodes to process_list.
While there exist connected nodes in graph that are not IN_GADAG
Select a new ear. Let its endpoints be X and Y.
If Y is root or (Y<<X)
Add the ear towards X to the ADAG
Else // (a) X is root, or (b) X<<Y, or (c) X, Y not ordered
Add the ear towards Y to the ADAG
Figure 6: Generic Algorithm to Find Ears and Their Direction in
2Connected Graph
The algorithm in Figure 6 merely requires that a cycle or ear be
selected without specifying how. Regardless of the method for
selecting the path, we will get an ADAG. The method used for finding
and selecting the ears is important; shorter ears result in shorter
paths along the MRTs. The MRT Lowpoint algorithm uses the Lowpoint
Inheritance method for constructing an ADAG (and ultimately a GADAG).
This method is defined in Section 5.5. Other methods for
constructing GADAGs are described in Appendices B and C. An
evaluation of these different methods is given in Section 8.
As an example, consider Figure 5 again. First, we select the
shortest cycle containing R, which can be RABFDE (uniform link
costs were assumed), so we get to the situation depicted in
Figure 5(b). Finally, we find a node next to a ready node; that must
be node C and assume we reached it from ready node B. We search a
path from C to R without B in the original graph. The first ready
node along this is node D, so the open ear is BCD. Since B<<D, we
add arc B>C and C>D to the ADAG. Since all the nodes are ready, we
stop at this point.
4.3. Lowpoint Values and Their Uses
A basic way of computing a spanning tree on a network graph is to run
a DFS, such as given in Figure 7. This tree has the important
property that if there is a link (x, n), then either n is a DFS
ancestor of x or n is a DFS descendant of x. In other words, either
n is on the path from the root to x or x is on the path from the root
to n.
global_variable: dfs_number
DFS_Visit(node x, node parent)
D(x) = dfs_number
dfs_number += 1
x.dfs_parent = parent
for each link (x, w)
if D(w) is not set
DFS_Visit(w, x)
Run_DFS(node gadag_root)
dfs_number = 0
DFS_Visit(gadag_root, NONE)
Figure 7: Basic DFS Algorithm
Given a node x, one can compute the minimal DFS number of the
neighbors of x, i.e., min( D(w) if (x,w) is a link). This gives the
earliest attachment point neighboring x. What is interesting,
though, is the earliest attachment point from x and x's descendants.
This is what is determined by computing the Lowpoint value.
In order to compute the low point value, the network is traversed
using DFS and the vertices are numbered based on the DFS walk. Let
this number be represented as DFS(x). All the edges that lead to
alreadyvisited nodes during DFS walk are backedges. The backedges
are important because they give information about reachability of a
node via another path.
The low point number is calculated by finding:
Low(x) = Minimum of ( (DFS(x),
Lowest DFS(n, x>n is a backedge),
Lowest Low(n, x>n is tree edge in DFS walk) ).
A detailed algorithm for computing the lowpoint value is given in
Figure 8. Figure 9 illustrates how the Lowpoint algorithm applies to
an example graph.
global_variable: dfs_number
Lowpoint_Visit(node x, node parent, interface p_to_x)
D(x) = dfs_number
L(x) = D(x)
dfs_number += 1
x.dfs_parent = parent
x.dfs_parent_intf = p_to_x.remote_intf
x.lowpoint_parent = NONE
for each ordered_interface intf of x
if D(intf.remote_node) is not set
Lowpoint_Visit(intf.remote_node, x, intf)
if L(intf.remote_node) < L(x)
L(x) = L(intf.remote_node)
x.lowpoint_parent = intf.remote_node
x.lowpoint_parent_intf = intf
else if intf.remote_node is not parent
if D(intf.remote_node) < L(x)
L(x) = D(intf.remote_node)
x.lowpoint_parent = intf.remote_node
x.lowpoint_parent_intf = intf
Run_Lowpoint(node gadag_root)
dfs_number = 0
Lowpoint_Visit(gadag_root, NONE, NONE)
Figure 8: Computing Lowpoint Value
[E] [J][I] [P][O]
     
     
[R] [D][C][F] [H][K] [N]
     
     
[A][B] [G] [L][M]
(a) a non2connected graph
[E] [J][I] [P][O]
(5, )  (10, ) (9, ) (16, ) (15, )
     
     
[R] [D][C][F] [H][K] [N]
(0, ) (4, ) (3, ) (6, ) (8, ) (11, ) (14, )
     
     
[A][B] [G] [L][M]
(1, ) (2, ) (7, ) (12, ) (13, )
(b) with DFS values assigned (D(x), L(x))
[E] [J][I] [P][O]
(5,0)  (10,3) (9,3) (16,11) (15,11)
     
     
[R] [D][C][F] [H][K] [N]
(0,0) (4,0) (3,0) (6,3) (8,3) (11,11) (14,11)
     
     
[A][B] [G] [L][M]
(1,0) (2,0) (7,3) (12,11) (13,11)
(c) with lowpoint values assigned (D(x), L(x))
Figure 9: Example Lowpoint Value Computation
From the lowpoint value and lowpoint parent, there are three very
useful things that motivate our computation.
First, if there is a child c of x such that L(c) >= D(x), then there
are no paths in the network graph that go from c or its descendants
to an ancestor of x; therefore, x is a cutvertex. In Figure 9, this
can be seen by looking at the DFS children of C. C has two children,
D and F and L(F) = 3 = D(C); so, it is clear that C is a cutvertex
and F is in a block where C is the block's root. L(D) = 0<3 = D(C),
so D has a path to the ancestors of C; in this case, D can go via E
to reach R. Comparing the lowpoint values of all a node's DFS
children with the node's DFSvalue is very useful because it allows
identification of the cutvertices and thus the blocks.
Second, by repeatedly following the path given by lowpoint_parent,
there is a path from x back to an ancestor of x that does not use the
link [x, x.dfs_parent] in either direction. The full path need not
be taken, but this gives a way of finding an initial cycle and then
ears.
Third, as seen in Figure 9, even if L(x)<D(x), there may be a block
that contains both the root and a DFSchild of a node while other
DFSchildren might be in different blocks. In this example, C's
child D is in the same block as R while F is not. It is important to
realize that the root of a block may also be the root of another
block.
4.4. Blocks in a Graph
A key idea for the MRT Lowpoint algorithm is that any non2connected
graph is made up by blocks (e.g., 2connected clusters, cutlinks,
and/or isolated nodes). To compute GADAGs and thus MRTs, computation
is done in each block to compute ADAGs or Redundant Trees and then
those ADAGs or Redundant Trees are combined into a GADAG or MRT.
[E] [J][I] [P][O]
     
     
[R] [D][C][F] [H][K] [N]
     
     
[A][B] [G] [L][M]
(a) A graph with four blocks:
three 2connected clusters
and one cutlink
[E]< [J]<[I] [P]<[O]
   ^  ^
V  V  V 
[R] [D]<[C] [F] [H]<[K] [N]
^  ^ ^
 V  
[A]>[B] [G] [L]>[M]
(b) MRTBlue for destination R
[E] [J]>[I] [P]>[O]
  
V V V
[R] [D]>[C]<[F] [H]<[K] [N]
^  ^  ^ 
 V    V
[A]<[B] [G]< [L]<[M]
(c) MRTRed for destination R
Figure 10
Consider the example depicted in Figure 10 (a). In this figure, a
special graph is presented, showing us all the ways 2connected
clusters can be connected. It has four blocks: block 1 contains R,
A, B, C, D, E; block 2 contains C, F, G, H, I, J; block 3 contains K,
L, M, N, O, P; and block 4 is a cutlink containing H and K. As can
be observed, the first two blocks have one common node (node C) and
blocks 2 and 3 do not have any common node, but they are connected
through a cutlink that is block 4. No two blocks can have more than
one common node, since two blocks with at least two common nodes
would qualify as a single 2connected cluster.
Moreover, observe that if we want to get from one block to another,
we must use a cutvertex (the cutvertices in this graph are C, H,
K), regardless of the path selected, so we can say that all the paths
from block 3 along the MRTs rooted at R will cross K first. This
observation means that if we want to find a pair of MRTs rooted at R,
then we need to build up a pair of RTs in block 3 with K as a root.
Similarly, we need to find another pair of RTs in block 2 with C as a
root, and finally, we need the last pair of RTs in block 1 with R as
a root. When all the trees are selected, we can simply combine them;
when a block is a cutlink (as in block 4), that cutlink is added in
the same direction to both of the trees. The resulting trees are
depicted in Figure 10 (b) and (c).
Similarly, to create a GADAG it is sufficient to compute ADAGs in
each block and connect them.
It is necessary, therefore, to identify the cutvertices, the blocks
and identify the appropriate localroot to use for each block.
4.5. Determining Localroot and Assigning BlockID
Each node in a network graph has a localroot, which is the cutvertex
(or root) in the same block that is closest to the root. The
localroot is used to determine whether two nodes share a common
block.
Compute_Localroot(node x, node localroot)
x.localroot = localroot
for each DFS child node c of x
if L(c) < D(x) //x is not a cutvertex
Compute_Localroot(c, x.localroot)
else
mark x as cutvertex
Compute_Localroot(c, x)
Compute_Localroot(gadag_root, gadag_root)
Figure 11: A Method for Computing Localroots
There are two different ways of computing the localroot for each
node. The standalone method is given in Figure 11 and better
illustrates the concept; it is used by the GADAG construction methods
given in Appendices B and C. The MRT Lowpoint algorithm computes the
localroot for a block as part of computing the GADAG using lowpoint
inheritance; the essence of this computation is given in Figure 12.
Both methods for computing the localroot produce the same results.
Get the current node, s.
Compute an ear (either through lowpoint inheritance
or by following dfs parents) from s to a ready node e.
(Thus, s is not e, if there is such ear.)
if s is e
for each node x in the ear that is not s
x.localroot = s
else
for each node x in the ear that is not s or e
x.localroot = e.localroot
Figure 12: EarBased Method for Computing Localroots
Once the localroots are known, two nodes X and Y are in a common
block if and only if one of the following three conditions apply.
o Y's localroot is X's localroot : They are in the same block and
neither is the cutvertex closest to the root.
o Y's localroot is X: X is the cutvertex closest to the root for
Y's block
o Y is X's localroot: Y is the cutvertex closest to the root for
X's block
Once we have computed the localroot for each node in the network
graph, we can assign for each node, a BlockID that represents the
block in which the node is present. This computation is shown in
Figure 13.
global_var: max_block_id
Assign_Block_ID(x, cur_block_id)
x.block_id = cur_block_id
foreach DFS child c of x
if (c.local_root is x)
max_block_id += 1
Assign_Block_ID(c, max_block_id)
else
Assign_Block_ID(c, cur_block_id)
max_block_id = 0
Assign_Block_ID(gadag_root, max_block_id)
Figure 13: Assigning BlockID to Identify Blocks
5. MRT Lowpoint Algorithm Specification
The MRT Lowpoint algorithm computes one GADAG that is then used by a
router to determine its MRTBlue and MRTRed next hops to all
destinations. Finally, based upon that information, alternates are
selected for each next hop to each destination. The different parts
of this algorithm are described below.
o Order the interfaces in the network graph. See Section 5.1.
o Compute the local MRT Island for the particular MRT Profile. See
Section 5.2.
o Select the root to use for the GADAG. See Section 5.3.
o Initialize all interfaces to UNDIRECTED. See Section 5.4.
o Compute the DFS value, e.g., D(x), and lowpoint value, L(x). See
Figure 8.
o Construct the GADAG. See Section 5.5.
o Assign directions to all interfaces that are still UNDIRECTED.
See Section 5.6.
o From the computing router x, compute the next hops for the MRT
Blue and MRTRed. See Section 5.7.
o Identify alternates for each next hop to each destination by
determining which one of the MRTBlue and the MRTRed the
computing router x should select. See Section 5.8.
A Python implementation of this algorithm is given in Appendix A.
5.1. Interface Ordering
To ensure consistency in computation, all routers MUST order
interfaces identically down to the set of links with the same metric
to the same neighboring node. This is necessary for the DFS in
Lowpoint_Visit in Section 4.3, where the selection order of the
interfaces to explore results in different trees. Consistent
interface ordering is also necessary for computing the GADAG, where
the selection order of the interfaces to use to form ears can result
in different GADAGs. It is also necessary for the topological sort
described in Section 5.8, where different topological sort orderings
can result in undirected links being added to the GADAG in different
directions.
The required ordering between two interfaces from the same router x
is given in Figure 14.
Interface_Compare(interface a, interface b)
if a.metric < b.metric
return A_LESS_THAN_B
if b.metric < a.metric
return B_LESS_THAN_A
if a.neighbor.mrt_node_id < b.neighbor.mrt_node_id
return A_LESS_THAN_B
if b.neighbor.mrt_node_id < a.neighbor.mrt_node_id
return B_LESS_THAN_A
// Same metric to same node, so the order doesn't matter for
// interoperability.
return A_EQUAL_TO_B
Figure 14: Rules for Ranking Multiple Interfaces (Order Is from Low
to High)
In Figure 14, if two interfaces on a router connect to the same
remote router with the same metric, the Interface_Compare function
returns A_EQUAL_TO_B. This is because the order in which those
interfaces are initially explored does not affect the final GADAG
produced by the algorithm described here. While only one of the
links will be added to the GADAG in the initial traversal, the other
parallel links will be added to the GADAG with the same direction
assigned during the procedure for assigning direction to UNDIRECTED
links described in Section 5.6. An implementation is free to apply
some additional criteria to break ties in interface ordering in this
situation, but those criteria are not specified here since they will
not affect the final GADAG produced by the algorithm.
The Interface_Compare function in Figure 14 relies on the
interface.metric and the interface.neighbor.mrt_node_id values to
order interfaces. The exact source of these values for different
IGPs and applications is specified in Figure 15. The metric and
mrt_node_id values for OSPFv2, OSPFv3, and ISIS provided here is
normative. The metric and mrt_node_id values for ISIS Path Control
and Reservation (PCR) in this table should be considered
informational. The normative values are specified in [IEEE8021Qca].
++++
 IGP/flooding  mrt_node_id  metric of 
 protocol  of neighbor  interface 
 and  on interface  
 application   
++++
 OSPFv2 for  4octet Neighbor  2octet Metric field 
 IP/LDP FRR  Router ID in  for corresponding 
  Link ID field for  pointtopoint link 
  corresponding  in RouterLSA 
  pointtopoint link  
  in RouterLSA  
++++
 OSPFv3 for  4octet Neighbor  2octet Metric field 
 IP/LDP FRR  Router ID field  for corresponding 
  for corresponding  pointtopoint link 
  pointtopoint link  in RouterLSA 
  in RouterLSA  
++++
 ISIS for  7octet neighbor  3octet metric field 
 IP/LDP FRR  system ID and  in Extended IS 
  pseudonode number  Reachability TLV (type 22) 
  in Extended IS  or MultiTopology 
  Reachability TLV (type IS Neighbor TLV (type 222) 
  22) or MultiTopology  
  IS Neighbor TLV (type  
  222)  
++++
 ISIS PCR for 8octet Bridge ID  3octet SPBLINKMETRIC in 
 protection  created from 2octet  SPBMetric subTLV (type 29)
 of traffic  Bridge Priority in  in Extended IS Reachability 
 in bridged  Shortest Path Bridging TLV (type 22) or 
 SPB Instance subTLV  MultiTopology 
 networks  (type 1) carried in  Intermediate Systems 
  MTCapability TLV  TLV (type 222). In the case
  (type 144) and 6octet of asymmetric link metrics, 
  neighbor system ID in  the larger link metric 
  Extended IS  is used for both link 
  Reachability TLV (type directions. 
  22) or MultiTopology  (informational) 
  Intermediate Systems  
  TLV (type 222)  
  (informational)  
++++
Figure 15: Value of interface.neighbor.mrt_node_id and
interface.metric to Be Used for Ranking Interfaces, for Different
Flooding Protocols and Applications
The metrics are unsigned integers and MUST be compared as unsigned
integers. The results of mrt_node_id comparisons MUST be the same as
would be obtained by converting the mrt_node_ids to unsigned integers
using network byte order and performing the comparison as unsigned
integers. In the case of ISIS for IP/LDP FRR with pointtopoint
links, the pseudonode number (the 7th octet) is zero. Broadcast
interfaces will be discussed in Section 7.
5.2. MRT Island Identification
The local MRT Island for a particular MRT profile can be determined
by starting from the computing router in the network graph and doing
a breadthfirstsearch (BFS). The BFS explores only links that are
in the same area/level, are not IGPexcluded, and are not MRT
ineligible. The BFS explores only nodes that support the particular
MRT profile. See Section 7 of [RFC7812] for moreprecise definitions
of these criteria.
MRT_Island_Identification(topology, computing_rtr, profile_id, area)
for all routers in topology
rtr.IN_MRT_ISLAND = FALSE
computing_rtr.IN_MRT_ISLAND = TRUE
explore_list = { computing_rtr }
while (explore_list is not empty)
next_rtr = remove_head(explore_list)
for each intf in next_rtr
if (not intf.IN_MRT_ISLAND
and not intf.MRTineligible
and not intf.remote_intf.MRTineligible
and not intf.IGPexcluded and (intf in area)
and (intf.remote_node supports profile_id) )
intf.IN_MRT_ISLAND = TRUE
intf.remote_intf.IN_MRT_ISLAND = TRUE
if (not intf.remote_node.IN_MRT_ISLAND))
intf.remote_node.IN_MRT_ISLAND = TRUE
add_to_tail(explore_list, intf.remote_node)
Figure 16: MRT Island Identification
5.3. GADAG Root Selection
In Section 8.3 of [RFC7812], the GADAG Root Selection Policy is
described for the Default MRT Profile. This selection policy allows
routers to consistently select a common GADAG Root inside the local
MRT Island, based on advertised priority values. The MRT Lowpoint
algorithm simply requires that all routers in the MRT Island MUST
select the same GADAG Root; the mechanism can vary based upon the MRT
profile description. Before beginning computation, the network graph
is reduced to contain only the set of routers that support the
specific MRT profile whose MRTs are being computed.
As noted in Section 7, pseudonodes MUST NOT be considered for GADAG
root selection.
It is expected that an operator will designate a set of routers as
good choices for selection as GADAG root by setting the GADAG Root
Selection Priority for that set of routers to lower (more preferred)
numerical values. For guidance on setting the GADAG Root Selection
Priority values, refer to Section 9.1.
5.4. Initialization
Before running the algorithm, there is the standard type of
initialization to be done, such as clearing any computed DFSvalues,
lowpointvalues, DFS parents, lowpointparents, any MRTcomputed next
hops, and flags associated with algorithm.
It is assumed that a regular SPF computation has been run so that the
primary next hops from the computing router to each destination are
known. This is required for determining alternates at the last step.
Initially, all interfaces MUST be initialized to UNDIRECTED. Whether
they are OUTGOING, INCOMING, or both is determined when the GADAG is
constructed and augmented.
It is possible that some links and nodes will be marked using
standard IGP mechanisms to discourage or prevent transit traffic.
Section 7.3.1 of [RFC7812] describes how those links and nodes are
excluded from MRT Island formation.
MRTFRR also has the ability to advertise links MRTIneligible, as
described in Section 7.3.2 of [RFC7812]. These links are excluded
from the MRT Island and the GADAG. Computation of MRT next hops will
therefore not use any MRTineligible links. The MRT Lowpoint
algorithm does still need to consider MRTineligible links when
computing FRR alternates, because an MRTineligible link can still be
the shortestpath next hop to reach a destination.
When a broadcast interface is advertised as MRTineligible, then the
pseudonode representing the entire broadcast network MUST NOT be
included in the MRT Island. This is equivalent to excluding all of
the broadcast interfaces on that broadcast network from the MRT
Island.
5.5. Constructing the GADAG Using Lowpoint Inheritance
As discussed in Section 4.2, it is necessary to find ears from a node
x that is already in the GADAG (known as IN_GADAG). Two different
methods are used to find ears in the algorithm. The first is by
going to a DFSchild that is not IN_GADAG and then following the
chain of lowpoint parents until an IN_GADAG node is found. The
second is by going to a neighbor that is not IN_GADAG and then
following the chain of DFS parents until an IN_GADAG node is found.
As an ear is found, the associated interfaces are marked based on the
direction taken. The nodes in the ear are marked as IN_GADAG. In
the algorithm, first the ears via DFSchildren are found and then the
ears via DFSneighbors are found.
By adding both types of ears when an IN_GADAG node is processed, all
ears that connect to that node are found. The order in which the
IN_GADAG nodes are processed is, of course, key to the algorithm.
The order is a stack of ears so the most recent ear is found at the
top of the stack. Of course, the stack stores nodes and not ears, so
an ordered list of nodes, from the first node in the ear to the last
node in the ear, is created as the ear is explored and then that list
is pushed onto the stack.
Each ear represents a partial order (see Figure 4) and processing the
nodes in order along each ear ensures that all ears connecting to a
node are found before a node higher in the partial order has its ears
explored. This means that the direction of the links in the ear is
always from the node x being processed towards the other end of the
ear. Additionally, by using a stack of ears, this means that any
unprocessed nodes in previous ears can only be ordered higher than
nodes in the ears below it on the stack.
In this algorithm that depends upon Lowpoint inheritance, it is
necessary that every node has a lowpoint parent that is not itself.
If a node is a cutvertex, that may not yet be the case. Therefore,
any nodes without a lowpoint parent will have their lowpoint parent
set to their DFS parent and their lowpoint value set to the DFSvalue
of their parent. This assignment also properly allows an ear between
two cutvertices.
Finally, the algorithm simultaneously computes each node's localroot,
as described in Figure 12. This is further elaborated as follows.
The localroot can be inherited from the node at the end of the ear
unless the end of the ear is x itself, in which case the localroot
for all the nodes in the ear would be x. This is because whenever
the first cycle is found in a block, or an ear involving a bridge is
computed, the cutvertex closest to the root would be x itself. In
all other scenarios, the properties of lowpoint/dfs parents ensure
that the end of the ear will be in the same block, and thus
inheriting its localroot would be the correct localroot for all newly
added nodes.
The pseudocode for the GADAG algorithm (assuming that the adjustment
of lowpoint for cutvertices has been made) is shown in Figure 17.
Construct_Ear(x, Stack, intf, ear_type)
ear_list = empty
cur_node = intf.remote_node
cur_intf = intf
not_done = true
while not_done
cur_intf.UNDIRECTED = false
cur_intf.OUTGOING = true
cur_intf.remote_intf.UNDIRECTED = false
cur_intf.remote_intf.INCOMING = true
if cur_node.IN_GADAG is false
cur_node.IN_GADAG = true
add_to_list_end(ear_list, cur_node)
if ear_type is CHILD
cur_intf = cur_node.lowpoint_parent_intf
cur_node = cur_node.lowpoint_parent
else // ear_type must be NEIGHBOR
cur_intf = cur_node.dfs_parent_intf
cur_node = cur_node.dfs_parent
else
not_done = false
if (ear_type is CHILD) and (cur_node is x)
// x is a cutvertex and the local root for
// the block in which the ear is computed
x.IS_CUT_VERTEX = true
localroot = x
else
// Inherit localroot from the end of the ear
localroot = cur_node.localroot
while ear_list is not empty
y = remove_end_item_from_list(ear_list)
y.localroot = localroot
push(Stack, y)
Construct_GADAG_via_Lowpoint(topology, gadag_root)
gadag_root.IN_GADAG = true
gadag_root.localroot = None
Initialize Stack to empty
push gadag_root onto Stack
while (Stack is not empty)
x = pop(Stack)
foreach ordered_interface intf of x
if ((intf.remote_node.IN_GADAG == false) and
(intf.remote_node.dfs_parent is x))
Construct_Ear(x, Stack, intf, CHILD)
foreach ordered_interface intf of x
if ((intf.remote_node.IN_GADAG == false) and
(intf.remote_node.dfs_parent is not x))
Construct_Ear(x, Stack, intf, NEIGHBOR)
Construct_GADAG_via_Lowpoint(topology, gadag_root)
Figure 17: Lowpoint Inheritance GADAG Algorithm
5.6. Augmenting the GADAG by Directing All Links
The GADAG, regardless of the method used to construct it, at this
point could be used to find MRTs, but the topology does not include
all links in the network graph. That has two impacts. First, there
might be shorter paths that respect the GADAG partial ordering and so
the alternate paths would not be as short as possible. Second, there
may be additional paths between a router x and the root that are not
included in the GADAG. Including those provides potentially more
bandwidth to traffic flowing on the alternates and may reduce
congestion compared to just using the GADAG as currently constructed.
The goal is thus to assign direction to every remaining link marked
as UNDIRECTED to improve the paths and number of paths found when the
MRTs are computed.
To do this, we need to establish a total order that respects the
partial order described by the GADAG. This can be done using Kahn's
topological sort [Kahn_1962_topo_sort], which essentially assigns a
number to a node x only after all nodes before it (e.g., with a link
incoming to x) have had their numbers assigned. The only issue with
the topological sort is that it works on DAGs and not ADAGs or
GADAGs.
To convert a GADAG to a DAG, it is necessary to remove all links that
point to a root of block from within that block. That provides the
necessary conversion to a DAG and then a topological sort can be
done. When adding undirected links to the GADAG, links connecting
the block root to other nodes in that block need special handling
because the topological order will not always give the right answer
for those links. There are three cases to consider. If the
undirected link in question has another parallel link between the
same two nodes that is already directed, then the direction of the
undirected link can be inherited from the previously directed link.
In the case of parallel cut links, we set all of the parallel links
to both INCOMING and OUTGOING. Otherwise, the undirected link in
question is set to OUTGOING from the block root node. A cutlink can
then be identified by the fact that it will be directed both INCOMING
and OUTGOING in the GADAG. The exact details of this whole process
are captured in Figure 18.
Add_Undirected_Block_Root_Links(topo, gadag_root)
foreach node x in topo
if x.IS_CUT_VERTEX or x is gadag_root
foreach interface i of x
if (i.remote_node.localroot is not x
or i.PROCESSED )
continue
Initialize bundle_list to empty
bundle.UNDIRECTED = true
bundle.OUTGOING = false
bundle.INCOMING = false
foreach interface i2 in x
if i2.remote_node is i.remote_node
add_to_list_end(bundle_list, i2)
if not i2.UNDIRECTED:
bundle.UNDIRECTED = false
if i2.INCOMING:
bundle.INCOMING = true
if i2.OUTGOING:
bundle.OUTGOING = true
if bundle.UNDIRECTED
foreach interface i3 in bundle_list
i3.UNDIRECTED = false
i3.remote_intf.UNDIRECTED = false
i3.PROCESSED = true
i3.remote_intf.PROCESSED = true
i3.OUTGOING = true
i3.remote_intf.INCOMING = true
else
if (bundle.OUTGOING and bundle.INCOMING)
foreach interface i3 in bundle_list
i3.UNDIRECTED = false
i3.remote_intf.UNDIRECTED = false
i3.PROCESSED = true
i3.remote_intf.PROCESSED = true
i3.OUTGOING = true
i3.INCOMING = true
i3.remote_intf.INCOMING = true
i3.remote_intf.OUTGOING = true
else if bundle.OUTGOING
foreach interface i3 in bundle_list
i3.UNDIRECTED = false
i3.remote_intf.UNDIRECTED = false
i3.PROCESSED = true
i3.remote_intf.PROCESSED = true
i3.OUTGOING = true
i3.remote_intf.INCOMING = true
else if bundle.INCOMING
foreach interface i3 in bundle_list
i3.UNDIRECTED = false
i3.remote_intf.UNDIRECTED = false
i3.PROCESSED = true
i3.remote_intf.PROCESSED = true
i3.INCOMING = true
i3.remote_intf.OUTGOING = true
Modify_Block_Root_Incoming_Links(topo, gadag_root)
foreach node x in topo
if x.IS_CUT_VERTEX or x is gadag_root
foreach interface i of x
if i.remote_node.localroot is x
if i.INCOMING:
i.INCOMING = false
i.INCOMING_STORED = true
i.remote_intf.OUTGOING = false
i.remote_intf.OUTGOING_STORED = true
Revert_Block_Root_Incoming_Links(topo, gadag_root)
foreach node x in topo
if x.IS_CUT_VERTEX or x is gadag_root
foreach interface i of x
if i.remote_node.localroot is x
if i.INCOMING_STORED
i.INCOMING = true
i.remote_intf.OUTGOING = true
i.INCOMING_STORED = false
i.remote_intf.OUTGOING_STORED = false
Run_Topological_Sort_GADAG(topo, gadag_root)
Modify_Block_Root_Incoming_Links(topo, gadag_root)
foreach node x in topo
node.unvisited = 0
foreach interface i of x
if (i.INCOMING)
node.unvisited += 1
Initialize working_list to empty
Initialize topo_order_list to empty
add_to_list_end(working_list, gadag_root)
while working_list is not empty
y = remove_start_item_from_list(working_list)
add_to_list_end(topo_order_list, y)
foreach ordered_interface i of y
if intf.OUTGOING
i.remote_node.unvisited = 1
if i.remote_node.unvisited is 0
add_to_list_end(working_list, i.remote_node)
next_topo_order = 1
while topo_order_list is not empty
y = remove_start_item_from_list(topo_order_list)
y.topo_order = next_topo_order
next_topo_order += 1
Revert_Block_Root_Incoming_Links(topo, gadag_root)
def Set_Other_Undirected_Links_Based_On_Topo_Order(topo)
foreach node x in topo
foreach interface i of x
if i.UNDIRECTED:
if x.topo_order < i.remote_node.topo_order
i.OUTGOING = true
i.UNDIRECTED = false
i.remote_intf.INCOMING = true
i.remote_intf.UNDIRECTED = false
else
i.INCOMING = true
i.UNDIRECTED = false
i.remote_intf.OUTGOING = true
i.remote_intf.UNDIRECTED = false
Add_Undirected_Links(topo, gadag_root)
Add_Undirected_Block_Root_Links(topo, gadag_root)
Run_Topological_Sort_GADAG(topo, gadag_root)
Set_Other_Undirected_Links_Based_On_Topo_Order(topo)
Add_Undirected_Links(topo, gadag_root)
Figure 18: Assigning Direction to UNDIRECTED Links
Proxynodes do not need to be added to the network graph. They
cannot be transited and do not affect the MRTs that are computed.
The details of how the MRTBlue and MRTRed next hops are computed
for proxynodes and how the appropriate alternate next hops are
selected is given in Section 5.9.
5.7. Compute MRT Next Hops
As was discussed in Section 4.1, once an ADAG is found, it is
straightforward to find the next hops from any node X to the ADAG
root. However, in this algorithm, we will reuse the common GADAG and
find not only the one pair of MRTs rooted at the GADAG root with it,
but find a pair rooted at each node. This is useful since it is
significantly faster to compute.
The method for computing differently rooted MRTs from the common
GADAG is based on two ideas. First, if two nodes X and Y are ordered
with respect to each other in the partial order, then an SPF along
OUTGOING links (an increasingSPF) and an SPF along INCOMING links (a
decreasingSPF) can be used to find the increasing and decreasing
paths. Second, if two nodes X and Y aren't ordered with respect to
each other in the partial order, then intermediary nodes can be used
to create the paths by increasing/decreasing to the intermediary and
then decreasing/increasing to reach Y.
As usual, the two basic ideas will be discussed assuming the network
is 2connected. The generalization to multiple blocks is discussed
in Section 5.7.4. The full algorithm is given in Section 5.7.5.
5.7.1. MRT Next Hops to All Nodes Ordered with Respect to the Computing
Node
Finding two nodedisjoint paths from the computing router X to any
node Y depends upon whether Y>>X or Y<<X. As shown in Figure 19, if
Y>>X, then there is an increasing path that goes from X to Y without
crossing R; this contains nodes in the interval [X,Y]. There is also
a decreasing path that decreases towards R and then decreases from R
to Y; this contains nodes in the interval [X,Rsmall] or [Rgreat,Y].
The two paths cannot have common nodes other than X and Y.
[Y]<(Cloud 2)< [X]
 ^
 
V 
(Cloud 3)>[R]>(Cloud 1)
MRTBlue path: X>Cloud 2>Y
MRTRed path: X>Cloud 1>R>Cloud 3>Y
Figure 19: Y>>X
Similar logic applies if Y<<X, as shown in Figure 20. In this case,
the increasing path from X increases to R and then increases from R
to Y to use nodes in the intervals [X,Rgreat] and [Rsmall, Y]. The
decreasing path from X reaches Y without crossing R and uses nodes in
the interval [Y,X].
[X]<(Cloud 2)< [Y]
 ^
 
V 
(Cloud 3)>[R]>(Cloud 1)
MRTBlue path: X>Cloud 3>R>Cloud 1>Y
MRTRed path: X>Cloud 2>Y
Figure 20: Y<<X
5.7.2. MRT Next Hops to All Nodes Not Ordered with Respect to the
Computing Node
When X and Y are not ordered, the first path should increase until we
get to a node G, where G>>Y. At G, we need to decrease to Y. The
other path should be just the opposite: we must decrease until we get
to a node H, where H<<Y, and then increase. Since R is smaller and
greater than Y, such G and H must exist. It is also easy to see that
these two paths must be node disjoint: the first path contains nodes
in interval [X,G] and [Y,G], while the second path contains nodes in
interval [H,X] and [H,Y]. This is illustrated in Figure 21. It is
necessary to decrease and then increase for the MRTBlue and increase
and then decrease for the MRTRed; if one simply increased for one
and decreased for the other, then both paths would go through the
root R.
(Cloud 6)<[Y]<(Cloud 5)<
 
 
V 
[G]>(Cloud 4)>[R]>(Cloud 1)>[H]
^ 
 
 
(Cloud 3)<[X]<(Cloud 2)<
MRTBlue path: decrease to H and increase to Y
X>Cloud 2>H>Cloud 5>Y
MRTRed path: increase to G and decrease to Y
X>Cloud 3>G>Cloud 6>Y
Figure 21: X and Y Unordered
This gives disjoint paths as long as G and H are not the same node.
Since G>>Y and H<<Y, if G and H could be the same node, that would
have to be the root R. This is not possible because there is only
one incoming interface to the root R that is created when the initial
cycle is found. Recall from Figure 6 that whenever an ear was found
to have an end that was the root R, the ear was directed from R so
that the associated interface on R is outgoing and not incoming.
Therefore, there must be exactly one node M that is the largest one
before R, so the MRTRed path will never reach R; it will turn at M
and decrease to Y.
5.7.3. Computing Redundant Tree Next Hops in a 2Connected Graph
The basic ideas for computing RT next hops in a 2connected graph
were given in Sections 5.7.1 and 5.7.2. Given these two ideas, how
can we find the trees?
If some node X only wants to find the next hops (which is usually the
case for IP networks), it is enough to find which nodes are greater
and less than X, and which are not ordered; this can be done by
running an increasingSPF and a decreasingSPF rooted at X and not
exploring any links from the ADAG root.
In principle, a traversal method other than SPF could be used to
traverse the GADAG in the process of determining blue and red next
hops that result in maximally redundant trees. This will be the case
as long as one traversal uses the links in the direction specified by
the GADAG and the other traversal uses the links in the direction
opposite of that specified by the GADAG. However, a different
traversal algorithm will generally result in different blue and red
next hops. Therefore, the algorithm specified here requires the use
of SPF to traverse the GADAG to generate MRT blue and red next hops,
as described below.
An increasingSPF rooted at X and not exploring links from the root
will find the increasing next hops to all Y>>X. Those increasing
next hops are X's next hops on the MRTBlue to reach Y. A
decreasingSPF rooted at X and not exploring links from the root will
find the decreasing next hops to all Z<<X. Those decreasing next
hops are X's next hops on the MRTRed to reach Z. Since the root R
is both greater than and less than X, after this increasingSPF and
decreasingSPF, X's next hops on the MRTBlue and on the MRTRed to
reach R are known. For every node Y>>X, X's next hops on the MRTRed
to reach Y are set to those on the MRTRed to reach R. For every
node Z<<X, X's next hops on the MRTBlue to reach Z are set to those
on the MRTBlue to reach R.
For those nodes that were not reached by either the increasingSPF or
the decreasingSPF, we can determine the next hops as well. The
increasing MRTBlue next hop for a node that is not ordered with
respect to X is the next hop along the decreasing MRTRed towards R,
and the decreasing MRTRed next hop is the next hop along the
increasing MRTBlue towards R. Naturally, since R is ordered with
respect to all the nodes, there will always be an increasing and a
decreasing path towards it. This algorithm does not provide the
complete specific path taken but just the appropriate next hops to
use. The identities of G and H are not determined by the computing
node X.
The final case to consider is when the GADAG root R computes its own
next hops. Since the GADAG root R is << all other nodes, running an
increasingSPF rooted at R will reach all other nodes; the MRTBlue
next hops are those found with this increasingSPF. Similarly, since
the GADAG root R is >> all other nodes, running a decreasingSPF
rooted at R will reach all other nodes; the MRTRed next hops are
those found with this decreasingSPF.
ED E<D<
    ^ 
   V  
R F C R F C
    ^ ^
   V  
AB A>B
(a) (b)
A 2connected graph A spanning ADAG rooted at R
Figure 22
As an example, consider the situation depicted in Figure 22. Node C
runs an increasingSPF and a decreasingSPF on the ADAG. The
increasingSPF reaches D, E, and R; the decreasingSPF reaches B, A,
and R. E>>C. So, towards E the MRTBlue next hop is D, since E was
reached on the increasing path through D. The MRTRed next hop
towards E is B, since R was reached on the decreasing path through B.
Since E>>D, D will similarly compute its MRTBlue next hop to be E,
ensuring that a packet on MRTBlue will use path CDE. B, A, and R
will similarly compute the MRTRed next hops towards E (which is
ordered less than B, A and R), ensuring that a packet on MRTRed will
use path CBARE.
C can determine the next hops towards F as well. Since F is not
ordered with respect to C, the MRTBlue next hop is the decreasing
one towards R (which is B) and the MRTRed next hop is the increasing
one towards R (which is D). Since F>>B, for its MRTBlue next hop
towards F, B will use the real increasing next hop towards F. So a
packet forwarded to B on MRTBlue will get to F on path CBF.
Similarly, D will use the real decreasing next hop towards F as its
MRTRed next hop, a packet on MRTRed will use path CDF.
5.7.4. Generalizing for a Graph That Isn't 2Connected
If a graph isn't 2connected, then the basic approach given in
Section 5.7.3 needs some extensions to determine the appropriate MRT
next hops to use for destinations outside the computing router X's
blocks. In order to find a pair of maximally redundant trees in that
graph, we need to find a pair of RTs in each of the blocks (the root
of these trees will be discussed later) and combine them.
When computing the MRT next hops from a router X, there are three
basic differences:
1. Only nodes in a common block with X should be explored in the
increasingSPF and decreasingSPF.
2. Instead of using the GADAG root, X's localroot should be used.
This has the following implications:
A. The links from X's localroot should not be explored.
B. If a node is explored in the outgoing SPF so Y>>X, then X's
MRTRed next hops to reach Y uses X's MRTRed next hops to
reach X's localroot and if Z<<X, then X's MRTBlue next hops
to reach Z uses X's MRTBlue next hops to reach X's
localroot.
C. If a node W in a common block with X was not reached in the
increasingSPF or decreasingSPF, then W is unordered with
respect to X. X's MRTBlue next hops to W are X's decreasing
(aka MRTRed) next hops to X's localroot. X's MRTRed next
hops to W are X's increasing (aka MRTBlue) next hops to X's
localroot.
3. For nodes in different blocks, the next hops must be inherited
via the relevant cutvertex.
These are all captured in the detailed algorithm given in
Section 5.7.5.
5.7.5. Complete Algorithm to Compute MRT Next Hops
The complete algorithm to compute MRT Next Hops for a particular
router X is given in Figure 23. In addition to computing the MRT
Blue next hops and MRTRed next hops used by X to reach each node Y,
the algorithm also stores an "order_proxy", which is the proper cut
vertex to reach Y if it is outside the block, and which is used later
in deciding whether the MRTBlue or the MRTRed can provide an
acceptable alternate for a particular primary next hop.
In_Common_Block(x, y)
if ( (x.block_id is y.block_id)
or (x is y.localroot) or (y is x.localroot) )
return true
return false
Store_Results(y, direction)
if direction is FORWARD
y.higher = true
y.blue_next_hops = y.next_hops
if direction is REVERSE
y.lower = true
y.red_next_hops = y.next_hops
SPF_No_Traverse_Block_Root(spf_root, block_root, direction)
Initialize spf_heap to empty
Initialize nodes' spf_metric to infinity and next_hops to empty
spf_root.spf_metric = 0
insert(spf_heap, spf_root)
while (spf_heap is not empty)
min_node = remove_lowest(spf_heap)
Store_Results(min_node, direction)
if ((min_node is spf_root) or (min_node is not block_root))
foreach interface intf of min_node
if ( ( ((direction is FORWARD) and intf.OUTGOING) or
((direction is REVERSE) and intf.INCOMING) )
and In_Common_Block(spf_root, intf.remote_node) )
path_metric = min_node.spf_metric + intf.metric
if path_metric < intf.remote_node.spf_metric
intf.remote_node.spf_metric = path_metric
if min_node is spf_root
intf.remote_node.next_hops = make_list(intf)
else
intf.remote_node.next_hops = min_node.next_hops
insert_or_update(spf_heap, intf.remote_node)
else if path_metric == intf.remote_node.spf_metric
if min_node is spf_root
add_to_list(intf.remote_node.next_hops, intf)
else
add_list_to_list(intf.remote_node.next_hops,
min_node.next_hops)
SetEdge(y)
if y.blue_next_hops is empty and y.red_next_hops is empty
SetEdge(y.localroot)
y.blue_next_hops = y.localroot.blue_next_hops
y.red_next_hops = y.localroot.red_next_hops
y.order_proxy = y.localroot.order_proxy
Compute_MRT_NextHops(x, gadag_root)
foreach node y
y.higher = y.lower = false
clear y.red_next_hops and y.blue_next_hops
y.order_proxy = y
SPF_No_Traverse_Block_Root(x, x.localroot, FORWARD)
SPF_No_Traverse_Block_Root(x, x.localroot, REVERSE)
// red and blue next hops are stored to x.localroot as different
// paths are found via the SPF and reverseSPF.
// Similarly, any node whose localroot is x will have its
// red_next_hops and blue_next_hops already set.
// Handle nodes in the same block that aren't the localroot
foreach node y
if (y.IN_MRT_ISLAND and (y is not x) and
(y.block_id is x.block_id) )
if y.higher
y.red_next_hops = x.localroot.red_next_hops
else if y.lower
y.blue_next_hops = x.localroot.blue_next_hops
else
y.blue_next_hops = x.localroot.red_next_hops
y.red_next_hops = x.localroot.blue_next_hops
// Inherit next hops and order_proxies to other components
if (x is not gadag_root) and (x.localroot is not gadag_root)
gadag_root.blue_next_hops = x.localroot.blue_next_hops
gadag_root.red_next_hops = x.localroot.red_next_hops
gadag_root.order_proxy = x.localroot
foreach node y
if (y is not gadag_root) and (y is not x) and y.IN_MRT_ISLAND
SetEdge(y)
max_block_id = 0
Assign_Block_ID(gadag_root, max_block_id)
Compute_MRT_NextHops(x, gadag_root)
Figure 23: Complete Algorithm to Compute MRT Next Hops
5.8. Identify MRT Alternates
At this point, a computing router S knows its MRTBlue next hops and
MRTRed next hops for each destination in the MRT Island. The
primary next hops along the SPT are also known. It remains to
determine for each primary next hop to a destination D, which MRT
avoids the primary nexthop node F. This computation depends upon
data set in Compute_MRT_NextHops such as each node y's
y.blue_next_hops, y.red_next_hops, y.order_proxy, y.higher, y.lower,
and topo_orders. Recall that any router knows only which are the
nodes greater and lesser than itself, but it cannot decide the
relation between any two given nodes easily; that is why we need
topological ordering.
For each primary nexthop node F to each destination D, S can call
Select_Alternates(S, D, F, primary_intf) to determine whether to use
the MRTBlue or MRTRed next hops as the alternate next hop(s) for
that primary next hop. The algorithm is given in Figure 24 and
discussed afterwards.
Select_Alternates_Internal(D, F, primary_intf,
D_lower, D_higher, D_topo_order):
if D_higher and D_lower
if F.HIGHER and F.LOWER
if F.topo_order < D_topo_order
return USE_RED
else
return USE_BLUE
if F.HIGHER
return USE_RED
if F.LOWER
return USE_BLUE
//F unordered wrt S
return USE_RED_OR_BLUE
else if D_higher
if F.HIGHER and F.LOWER
return USE_BLUE
if F.LOWER
return USE_BLUE
if F.HIGHER
if (F.topo_order > D_topo_order)
return USE_BLUE
if (F.topo_order < D_topo_order)
return USE_RED
//F unordered wrt S
return USE_RED_OR_BLUE
else if D_lower
if F.HIGHER and F.LOWER
return USE_RED
if F.HIGHER
return USE_RED
if F.LOWER
if F.topo_order > D_topo_order
return USE_BLUE
if F.topo_order < D_topo_order
return USE_RED
//F unordered wrt S
return USE_RED_OR_BLUE
else //D is unordered wrt S
if F.HIGHER and F.LOWER
if primary_intf.OUTGOING and primary_intf.INCOMING
return USE_RED_OR_BLUE
if primary_intf.OUTGOING
return USE_BLUE
if primary_intf.INCOMING
return USE_RED
//primary_intf not in GADAG
return USE_RED
if F.LOWER
return USE_RED
if F.HIGHER
return USE_BLUE
//F unordered wrt S
if F.topo_order > D_topo_order:
return USE_BLUE
else:
return USE_RED
Select_Alternates(D, F, primary_intf)
if not In_Common_Block(F, S)
return PRIM_NH_IN_DIFFERENT_BLOCK
if (D is F) or (D.order_proxy is F)
return PRIM_NH_IS_D_OR_OP_FOR_D
D_lower = D.order_proxy.LOWER
D_higher = D.order_proxy.HIGHER
D_topo_order = D.order_proxy.topo_order
return Select_Alternates_Internal(D, F, primary_intf,
D_lower, D_higher, D_topo_order)
Figure 24: Select_Alternates() and Select_Alternates_Internal()
It is useful to first handle the case where F is also D, or F is the
order proxy for D. In this case, only link protection is possible.
The MRT that doesn't use the failed primary next hop is used. If
both MRTs use the primary next hop, then the primary next hop must be
a cutlink, so either MRT could be used but the set of MRT next hops
must be pruned to avoid the failed primary nexthop interface. To
indicate this case, Select_Alternates returns
PRIM_NH_IS_D_OR_OP_FOR_D. Explicit pseudocode to handle the three
subcases above is not provided.
The logic behind Select_Alternates_Internal() is described in
Figure 25. As an example, consider the first case described in the
table, where the D>>S and D<<S. If this is true, then either S or D
must be the block root, R. If F>>S and F<<S, then S is the block
root. So the blue path from S to D is the increasing path to D, and
the red path S to D is the decreasing path to D. If the
F.topo_order>D.topo_order, then either F is ordered higher than D or
F is unordered with respect to D. Therefore, F is either on a
decreasing path from S to D, or it is on neither an increasing nor a
decreasing path from S to D. In either case, it is safe to take an
increasing path from S to D to avoid F. We know that when S is R,
the increasing path is the blue path, so it is safe to use the blue
path to avoid F.
If instead F.topo_order<D.topo_order, then either F is ordered lower
than D, or F is unordered with respect to D. Therefore, F is either
on an increasing path from S to D, or it is on neither an increasing
nor a decreasing path from S to D. In either case, it is safe to
take a decreasing path from S to D to avoid F. We know that when S
is R, the decreasing path is the red path, so it is safe to use the
red path to avoid F.
If F>>S or F<<S (but not both), then D is the block root. We then
know that the blue path from S to D is the increasing path to R, and
the red path is the decreasing path to R. When F>>S, we deduce that
F is on an increasing path from S to R. So in order to avoid F, we
use a decreasing path from S to R, which is the red path. Instead,
when F<<S, we deduce that F is on a decreasing path from S to R. So
in order to avoid F, we use an increasing path from S to R, which is
the blue path.
All possible cases are systematically described in the same manner in
the rest of the table.
++++++
 D  MRT blue  F  additional  F  Alternate 
 wrt  and red  wrt  criteria  wrt  
 S  path  S   MRT  
  properties    (deduced)  
+++++++
 D>>S  Blue path:  F>>S  additional  F on an  Use Red 
 and  Increasing  only  criteria  increasing  to avoid 
 D<<S, path to R.   not needed  path from  F 
 D is  Red path:    S to R  
 R,  Decreasing +++++
  path to R.  F<<S  additional  F on a  Use Blue 
   only  criteria  decreasing  to avoid 
    not needed  path from  F 
 or     S to R  
  +++++
   F>>S  topo(F)>topo(D)  F on a  Use Blue 
 S is  Blue path:  and  implies that  decreasing  to avoid 
 R  Increasing  F<<S, F>>D or F??D  path from  F 
  path to D.    S to D or  
  Red path:    neither  
  Decreasing  ++++
  path to D.   topo(F)<topo(D)  F on an  Use Red 
    implies that  increasing  to avoid 
    F<<D or F??D  path from  F 
     S to D or  
     neither  
  +++++
   F??S  Can only occur  F is on  Use Red 
    when link  neither  or Blue 
    between  increasing  to avoid 
    F and S  nor decr.  F 
    is marked  path from  
    MRT_INELIGIBLE  S to D or R 
+++++++
 D>>S  Blue path:  F<<S  additional  F on  Use Blue 
 only  Increasing  only  criteria  decreasing  to avoid 
  shortest   not needed  path from  F 
  path from    S to R  
  S to D. +++++
  Red path:  F>>S  topo(F)>topo(D)  F on  Use Blue 
  Decreasing  only  implies that  decreasing  to avoid 
  shortest   F>>D or F??D  path from  F 
  path from    R to D  
  S to R,    or  
  then    neither  
  decreasing  ++++
  shortest   topo(F)<topo(D)  F on  Use Red 
  path from   implies that  increasing  to avoid 
  R to D.   F<<D or F??D  path from  F 
     S to D  
     or  
     neither  
  +++++
   F>>S  additional  F on Red  Use Blue 
   and  criteria   to avoid 
   F<<S, not needed   F 
   F is    
   R    
  +++++
   F??S  Can only occur  F is on  Use Red 
    when link  neither  or Blue 
    between  increasing  to avoid 
    F and S  nor decr.  F 
    is marked  path from  
    MRT_INELIGIBLE  S to D or R 
+++++++
 D<<S  Blue path:  F>>S  additional  F on  Use Red 
 only  Increasing  only  criteria  increasing  to avoid 
  shortest   not needed  path from  F 
  path from    S to R  
  S to R, +++++
  then  F<<S  topo(F)>topo(D)  F on  Use Blue 
  increasing  only  implies that  decreasing  to avoid 
  shortest   F>>D or F??D  path from  F 
  path from    R to D  
  R to D.    or  
  Red path:    neither  
  Decreasing  ++++
  shortest   topo(F)<topo(D)  F on  Use Red 
  path from   implies that  increasing  to avoid 
  S to D.   F<<D or F??D  path from  F 
     S to D  
     or  
     neither  
  +++++
   F>>S  additional  F on Blue  Use Red 
   and  criteria   to avoid 
   F<<S, not   F 
   F is  needed   
   R    
  +++++
   F??S  Can only occur  F is on  Use Red 
    when link  neither  or Blue 
    between  increasing  to avoid 
    F and S  nor decr.  F 
    is marked  path from  
    MRT_INELIGIBLE  S to D or R 
+++++++
 D??S  Blue path:  F<<S  additional  F on a  Use Red 
  Decr. from  only  criteria  decreasing  to avoid 
  S to first   not needed  path from  F 
  node K<<D,    S to K.  
  then incr. +++++
  to D.  F>>S  additional  F on an  Use Blue 
  Red path:  only  criteria  increasing  to avoid 
  Incr. from   not needed  path from  F 
  S to first    S to L  
  node L>>D,     
  then decr.     
  +++++
   F??S  topo(F)>topo(D)  F on decr.  Use Blue 
    implies that  path from  to avoid 
    F>>D or F??D  L to D or  F 
     neither  
   ++++
    topo(F)<topo(D)  F on incr.  Use Red 
    implies that  path from  to avoid 
    F<<D or F??D  K to D or  F 
     neither  
  +++++
   F>>S  GADAG link  F on an  Use Blue 
   and  direction  incr. path  to avoid 
   F<<S, S>F  from S  F 
   F is ++++
   R  GADAG link  F on a  Use Red 
    direction  decr. path  to avoid 
    S<F  from S  F 
   ++++
    GADAG link  Either F is the order 
    direction  proxy for D (case 
    S<>F  already handled) or D 
     is in a different block 
     from F, in which case 
     Red or Blue avoids F 
   +++
    SF link not  Relies on special 
    in GADAG,  construction of GADAG 
    only when  to demonstrate that 
    SF link is  using Red avoids F 
    MRT_INELIGIBLE  (see text) 
++++++
Determining MRT next hops and alternates based on the partial order
and topological sort relationships between the source(S),
destination(D), primary next hop(F), and block root(R). topo(N)
indicates the topological sort value of node N. X??Y indicates that
node X is unordered with respect to node Y. It is assumed that the
case where F is D, or where F is the order proxy for D, has already
been handled.
Figure 25: Determining MRT Next Hops and Alternates
The last case in Figure 25 requires additional explanation. The fact
that the red path from S to D in this case avoids F relies on a
special property of the GADAGs that we have constructed in this
algorithm, a property not shared by all GADAGs in general. When D is
unordered with respect to S, and F is the localroot for S, it can
occur that the link between S and F is not in the GADAG only when
that link has been marked MRT_INELIGIBLE. For an arbitrary GADAG, S
doesn't have enough information based on the computed order
relationships to determine if the red path or blue path will hit F
(which is also the localroot) before hitting K or L, and making it
safely to D. However, the GADAGs that we construct using the
algorithm in this document are not arbitrary GADAGs. They have the
additional property that incoming links to a localroot come from only
one other node in the same block. This is a result of the method of
construction. This additional property guarantees that the red path
from S to D will never pass through the localroot of S. (That would
require the localroot to play the role of L, the first node in the
path ordered higher than D, which would in turn require the localroot
to have two incoming links in the GADAG, which cannot happen.)
Therefore, it is safe to use the red path to avoid F with these
specially constructed GADAGs.
As an example of how Select_Alternates_Internal() operates, consider
the ADAG depicted in Figure 26 and first suppose that G is the
source, D is the destination, and H is the failed next hop. Since
D>>G, we need to compare H.topo_order and D.topo_order. Since
D.topo_order>H.topo_order, D must be either higher than H or
unordered with respect to H, so we should select the decreasing path
towards the root. If, however, the destination were instead J, we
must find that H.topo_order>J.topo_order, so we must choose the
increasing Blue next hop to J, which is I. In the case, when instead
the destination is C, we find that we need to first decrease to avoid
using H, so the Blue, first decreasing then increasing, path is
selected.
[E]<[D]<[H]<[J]
 ^ ^ ^
V   
[R] [C] [G]>[I]
 ^ ^ ^
V   
[A]>[B]>[F]
Figure 26: ADAG Rooted at R for a 2Connected Graph
5.9. Named ProxyNodes
As discussed in Section 11.2 of [RFC7812], it is necessary to find
MRTBlue and MRTRed next hops and MRTFRR alternates for named
proxynodes. An example use case is for a router that is not part of
that local MRT Island, when there is only partial MRT support in the
domain.
5.9.1. Determining ProxyNode Attachment Routers
Section 11.2 of [RFC7812] discusses general considerations for
determining the two proxynode attachment routers for a given proxy
node, corresponding to a prefix. A router in the MRT Island that
advertises the prefix is a candidate for being a proxynode
attachment router, with the associated namedproxycost equal to the
advertised cost to the prefix.
An Island Border Router (IBR) is a router in the MRT Island that is
connected to an Island Neighbor (IN), which is a router not in the
MRT Island but in the same area/level. An (IBR,IN) pair is a
candidate for being a proxynode attachment router, if the shortest
path from the IN to the prefix does not enter the MRT Island. A
method for identifying such LoopFree Island Neighbors (LFINs) is
given below. The namedproxycost assigned to each (IBR, IN) pair is
cost(IBR, IN) + D_opt(IN, prefix).
From the set of prefixadvertising routers and the set of IBRs with
at least one LFIN, the two routers with the lowest namedproxycost
are selected. Ties are broken based upon the lowest Router ID. For
ease of discussion, the two selected routers will be referred to as
proxynode attachment routers.
5.9.2. Computing If an Island Neighbor (IN) Is LoopFree
As discussed above, the IN needs to be loopfree with respect to the
whole MRT Island for the destination. This can be accomplished by
running the usual SPF algorithm while keeping track of which shortest
paths have passed through the MRT island. Pseudocode for this is
shown in Figure 27. The Island_Marking_SPF() is run for each IN that
needs to be evaluated for the loopfree condition, with the IN as the
spf_root. Whether or not an IN is loopfree with respect to the MRT
island can then be determined by evaluating node.PATH_HITS_ISLAND for
each destination of interest.
Island_Marking_SPF(spf_root)
Initialize spf_heap to empty
Initialize nodes' spf_metric to infinity and next_hops to empty
and PATH_HITS_ISLAND to false
spf_root.spf_metric = 0
insert(spf_heap, spf_root)
while (spf_heap is not empty)
min_node = remove_lowest(spf_heap)
foreach interface intf of min_node
path_metric = min_node.spf_metric + intf.metric
if path_metric < intf.remote_node.spf_metric
intf.remote_node.spf_metric = path_metric
if min_node is spf_root
intf.remote_node.next_hops = make_list(intf)
else
intf.remote_node.next_hops = min_node.next_hops
if intf.remote_node.IN_MRT_ISLAND
intf.remote_node.PATH_HITS_ISLAND = true
else
intf.remote_node.PATH_HITS_ISLAND =
min_node.PATH_HITS_ISLAND
insert_or_update(spf_heap, intf.remote_node)
else if path_metric == intf.remote_node.spf_metric
if min_node is spf_root
add_to_list(intf.remote_node.next_hops, intf)
else
add_list_to_list(intf.remote_node.next_hops,
min_node.next_hops)
if intf.remote_node.IN_MRT_ISLAND
intf.remote_node.PATH_HITS_ISLAND = true
else
intf.remote_node.PATH_HITS_ISLAND =
min_node.PATH_HITS_ISLAND
Figure 27: Island_Marking_SPF() for Determining If an Island Neighbor
Is LoopFree
It is also possible that a given prefix is originated by a
combination of nonisland routers and island routers. The results of
the Island_Marking_SPF() computation can be used to determine if the
shortest path from an IN to reach that prefix hits the MRT Island.
The shortest path for the IN to reach prefix P is determined by the
total cost to reach prefix P, which is the sum of the cost for the IN
to reach a prefixadvertising node and the cost with which that node
advertises the prefix. The path with the minimum total cost to
prefix P is chosen. If the prefixadvertising node for that minimum
total cost path has PATH_HITS_ISLAND set to True, then the IN is not
loopfree with respect to the MRT Island for reaching prefix P. If
there are multiple minimum total cost paths to reach prefix P, then
all of the prefixadvertising routers involved in the minimum total
cost paths MUST have PATH_HITS_ISLAND set to False for the IN to be
considered loopfree to reach P.
Note that there are other computations that could be used to
determine if paths from a given IN _might_ pass through the MRT
Island for a given prefix or destination. For example, a previous
draft version of this document specified running the SPF algorithm on
modified topology that treats the MRT Island as a single node (with
intraisland links set to zero cost) in order to provide input to
computations to determine if the path from IN to nonisland
destination hits the MRT Island in this modified topology. This
computation is enough to guarantee that a path will not hit the MRT
Island in the original topology. However, it is possible that a path
that is disqualified for hitting the MRT Island in the modified
topology will not actually hit the MRT Island in the original
topology. The algorithm described in Island_Marking_SPF() above does
not modify the original topology, and will only disqualify a path if
the actual path does in fact hit the MRT Island.
Since all routers need to come to the same conclusion about which
routers qualify as LFINs, this specification requires that all
routers computing LFINs MUST use an algorithm whose result is
identical to that of the Island_Marking_SPF() in Figure 27.
5.9.3. Computing MRT Next Hops for ProxyNodes
Determining the MRT next hops for a proxynode in the degenerate case
where the proxynode is attached to only one node in the GADAG is
trivial, as all needed information can be derived from that proxy
node attachment router. If there are multiple interfaces connecting
the proxynode to the single proxynode attachment router, then some
can be assigned to MRTRed and others to MRT_Blue.
Now, consider the proxynode P that is attached to two proxynode
attachment routers. The pseudocode for Select_Proxy_Node_NHs(P,S) in
Figure 28 specifies how a computingrouter S MUST compute the MRT red
and blue next hops to reach proxynode P. The proxynode attachment
router with the lower value of mrt_node_id (as defined in Figure 15)
is assigned to X, and the other proxynode attachment router is
assigned to Y. We will be using the relative order of X,Y, and S in
the partial order defined by the GADAG to determine the MRT red and
blue next hops to reach P, so we also define A and B as the order
proxies for X and Y, respectively, with respect to S. The order
proxies for all nodes with respect to S were already computed in
Compute_MRT_NextHops().
def Select_Proxy_Node_NHs(P,S):
if P.pnar1.node.node_id < P.pnar2.node.node_id:
X = P.pnar1.node
Y = P.pnar2.node
else:
X = P.pnar2.node
Y = P.pnar1.node
P.pnar_X = X
P.pnar_Y = Y
A = X.order_proxy
B = Y.order_proxy
if (A is S.localroot
and B is S.localroot):
// case 1.0
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if (A is S.localroot
and B is not S.localroot):
// case 2.0
if B.LOWER:
// case 2.1
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if B.HIGHER:
// case 2.2
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
else:
// case 2.3
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if (A is not S.localroot
and B is S.localroot):
// case 3.0
if A.LOWER:
// case 3.1
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
if A.HIGHER:
// case 3.2
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
// case 3.3
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if (A is not S.localroot
and B is not S.localroot):
// case 4.0
if (S is A.localroot or S is B.localroot):
// case 4.05
if A.topo_order < B.topo_order:
// case 4.05.1
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
// case 4.05.2
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
if A.LOWER:
// case 4.1
if B.HIGHER:
// case 4.1.1
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
if B.LOWER:
// case 4.1.2
if A.topo_order < B.topo_order:
// case 4.1.2.1
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
// case 4.1.2.2
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
else:
// case 4.1.3
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if A.HIGHER:
// case 4.2
if B.HIGHER:
// case 4.2.1
if A.topo_order < B.topo_order:
// case 4.2.1.1
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
// case 4.2.1.2
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
if B.LOWER:
// case 4.2.2
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
// case 4.2.3
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
else:
// case 4.3
if B.LOWER:
// case 4.3.1
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if B.HIGHER:
// case 4.3.2
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
else:
// case 4.3.3
if A.topo_order < B.topo_order:
// case 4.3.3.1
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
// case 4.3.3.2
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
assert(False)
Figure 28: Select_Proxy_Node_NHs()
It is useful to understand up front that the blue next hops to reach
proxynode P produced by Select_Proxy_Node_NHs() will always be the
next hops that reach proxynode attachment router X, while the red
next hops to reach proxynode P will always be the next hops that
reach proxynode attachment router Y. This is different from the red
and blue next hops produced by Compute_MRT_NextHops() where, for
example, blue next hops to a destination that is ordered with respect
to the source will always correspond to an INCREASING next hop on the
GADAG. The exact choice of which next hops chosen by
Select_Proxy_Node_NHs() as the blue next hops to reach P (which will
necessarily go through X on its way to P) does depend on the GADAG,
but the relationship is more complex than was the case with
Compute_MRT_NextHops().
There are 21 different relative order relationships between A, B, and
S that Select_Proxy_Node_NHs() uses to determine red and blue next
hops to P. This document does not attempt to provide an exhaustive
description of each case considered in Select_Proxy_Node_NHs().
Instead, we provide a highlevel overview of the different cases, and
we consider a few cases in detail to give an example of the reasoning
that can be used to understand each case.
At the highest level, Select_Proxy_Node_NHs() distinguishes between
four different cases depending on whether or not A or B is the
localroot for S. For example, for case 4.0, neither A nor B is the
localroot for S. Case 4.05 addresses the case where S is the
localroot for either A or B, while cases 4.1, 4.2, and 4.3 address
the cases where A is ordered lower than S, A is ordered higher than
S, or A is unordered with respect to S on the GADAG. In general,
each of these cases is then further subdivided into whether or not B
is ordered lower than S, B is ordered higher than S, or B is
unordered with respect to S. In some cases, we also need a further
level of discrimination, where we use the topological sort order of A
with respect to B.
As a detailed example, let's consider case 4.1 and all of its sub
cases, and explain why the red and blue next hops to reach P are
chosen as they are in Select_Proxy_Node_NHs(). In case 4.1, neither
A nor B is the localroot for S, S is not the localroot for A or B,
and A is ordered lower than S on the GADAG. In this situation, we
know that the red path to reach X (as computed in
Compute_MRT_NextHops()) will follow DECREASING next hops towards A,
while the blue path to reach X will follow INCREASING next hops to
the localroot, and then INCREASING next hops to A.
Now consider subcase 4.1.1 where B is ordered higher than S. In
this situation, we know that the blue path to reach Y will follow
INCREASING next hops towards B, while the red next hops to reach Y
will follow DECREASING next hops to the localroot, and then
DECREASING next hops to B. So, to reach X and Y by two disjoint
paths, we can choose the red next hops to X and the blue next hops to
Y. We have chosen the convention that blue next hops to P are those
that pass through X, and red next hops to P are those that pass
through Y, so we can see that case 4.1.1 produces the desired result.
Choosing blue to X and red to Y does not produce disjoint paths
because the paths intersect at least at the localroot.
Now consider subcase 4.1.2 where B is ordered lower than S. In this
situation, we know that the red path to reach Y will follow
DECREASING next hops towards B, while the BLUE next hops to reach Y
will follow INCREASING next hops to the localroot, and then
INCREASING next hops to A. The choice here is more difficult than in
4.1.1 because A and B are both on the DECREASING path from S towards
the localroot. We want to use the direct DECREASING(red) path to the
one that is nearer to S on the GADAG. We get this extra information
by comparing the topological sort order of A and B. If
A.topo_order<B.topo_order, then we use red to Y and blue to X, since
the red path to Y will DECREASE to B without hitting A, and the blue
path to X will INCREASE to A without hitting B. Instead, if
A.topo_order>B.topo_order, then we use red to X and blue to Y.
Note that when A is unordered with respect to B, the result of
comparing A.topo_order with B.topo_order could be greater than or
less than. In this case, the result doesn't matter because either
choice (red to Y and blue to X or red to X and blue to Y) would work.
What is required is that all nodes in the network give the same
result when comparing A.topo_order with B.topo_order. This is
guaranteed by having all nodes run the same algorithm
(Run_Topological_Sort_GADAG()) to compute the topological sort order.
Finally, we consider case 4.1.3, where B is unordered with respect to
S. In this case, the blue path to reach Y will follow the DECREASING
next hops towards the localroot until it reaches some node (K) which
is ordered less than B, after which it will take INCREASING next hops
to B. The red path to reach Y will follow the INCREASING next hops
towards the localroot until it reaches some node (L) which is ordered
greater than B, after which it will take DECREASING next hops to B.
Both K and A are reached by DECREASING from S, but we don't have
information about whether or not that DECREASING path will hit K or A
first. Instead, we do know that the INCREASING path from S will hit
L before reaching A. Therefore, we use the red path to reach Y and
the red path to reach X.
Similar reasoning can be applied to understand the other 17 cases
used in Select_Proxy_Node_NHs(). However, cases 2.3 and 3.3 deserve
special attention because the correctness of the solution for these
two cases relies on a special property of the GADAGs that we have
constructed in this algorithm, a property not shared by all GADAGs in
general. Focusing on case 2.3, we consider the case where A is the
localroot for S, while B is not, and B is unordered with respect to
S. The red path to X DECREASES from S to the localroot A, while the
blue path to X INCREASES from S to the localroot A. The blue path to
Y DECREASES towards the localroot A until it reaches some node (K)
which is ordered less than B, after which the path INCREASES to B.
The red path to Y INCREASES towards the localroot A until it reaches
some node (L) which is ordered greater than B, after which the path
DECREASES to B. It can be shown that for an arbitrary GADAG, with
only the ordering relationships computed so far, we don't have enough
information to choose a pair of paths to reach X and Y that are
guaranteed to be disjoint. In some topologies, A will play the role
of K, the first node ordered less than B on the blue path to Y. In
other topologies, A will play the role of L, the first node ordered
greater than B on the red path to Y. The basic problem is that we
cannot distinguish between these two cases based on the ordering
relationships.
As discussed Section 5.8, the GADAGs that we construct using the
algorithm in this document are not arbitrary GADAGs. They have the
additional property that incoming links to a localroot come from only
one other node in the same block. This is a result of the method of
construction. This additional property guarantees that localroot A
will never play the role of L in the red path to Y, since L must have
at least two incoming links from different nodes in the same block in
the GADAG. This, in turn, allows Select_Proxy_Node_NHs() to choose
the red path to Y and the red path to X as the disjoint MRT paths to
reach P.
5.9.4. Computing MRT Alternates for ProxyNodes
After finding the red and the blue next hops for a given proxynode
P, it is necessary to know which one of these to use in the case of
failure. This can be done by Select_Alternates_Proxy_Node(), as
shown in the pseudocode in Figure 29.
def Select_Alternates_Proxy_Node(P,F,primary_intf):
S = primary_intf.local_node
X = P.pnar_X
Y = P.pnar_Y
A = X.order_proxy
B = Y.order_proxy
if F is A and F is B:
return 'PRIM_NH_IS_OP_FOR_BOTH_X_AND_Y'
if F is A:
return 'USE_RED'
if F is B:
return 'USE_BLUE'
if not In_Common_Block(A, B):
if In_Common_Block(F, A):
return 'USE_RED'
elif In_Common_Block(F, B):
return 'USE_BLUE'
else:
return 'USE_RED_OR_BLUE'
if (not In_Common_Block(F, A)
and not In_Common_Block(F, A) ):
return 'USE_RED_OR_BLUE'
alt_to_X = Select_Alternates(X, F, primary_intf)
alt_to_Y = Select_Alternates(Y, F, primary_intf)
if (alt_to_X == 'USE_RED_OR_BLUE'
and alt_to_Y == 'USE_RED_OR_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED_OR_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED_OR_BLUE':
return 'USE_RED'
if (A is S.localroot
and B is S.localroot):
// case 1.0
if (alt_to_X == 'USE_BLUE' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
if (A is S.localroot
and B is not S.localroot):
// case 2.0
if B.LOWER:
// case 2.1
if (alt_to_X == 'USE_BLUE' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
if B.HIGHER:
// case 2.2
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
else:
// case 2.3
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
if (A is not S.localroot
and B is S.localroot):
// case 3.0
if A.LOWER:
// case 3.1
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
if A.HIGHER:
// case 3.2
if (alt_to_X == 'USE_BLUE' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
// case 3.3
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
if (A is not S.localroot
and B is not S.localroot):
// case 4.0
if (S is A.localroot or S is B.localroot):
// case 4.05
if A.topo_order < B.topo_order:
// case 4.05.1
if (alt_to_X == 'USE_BLUE' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
// case 4.05.2
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
if A.LOWER:
// case 4.1
if B.HIGHER:
// case 4.1.1
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
if B.LOWER:
// case 4.1.2
if A.topo_order < B.topo_order:
// case 4.1.2.1
if (alt_to_X == 'USE_BLUE'
and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
// case 4.1.2.2
if (alt_to_X == 'USE_RED'
and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
else:
// case 4.1.3
if (F.LOWER and not F.HIGHER
and F.topo_order > A.topo_order):
// case 4.1.3.1
return 'USE_RED'
else:
// case 4.1.3.2
return 'USE_BLUE'
if A.HIGHER:
// case 4.2
if B.HIGHER:
// case 4.2.1
if A.topo_order < B.topo_order:
// case 4.2.1.1
if (alt_to_X == 'USE_BLUE'
and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
// case 4.2.1.2
if (alt_to_X == 'USE_RED'
and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
if B.LOWER:
// case 4.2.2
if (alt_to_X == 'USE_BLUE'
and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
// case 4.2.3
if (F.HIGHER and not F.LOWER
and F.topo_order < A.topo_order):
return 'USE_RED'
else:
return 'USE_BLUE'
else:
// case 4.3
if B.LOWER:
// case 4.3.1
if (F.LOWER and not F.HIGHER
and F.topo_order > B.topo_order):
return 'USE_BLUE'
else:
return 'USE_RED'
if B.HIGHER:
// case 4.3.2
if (F.HIGHER and not F.LOWER
and F.topo_order < B.topo_order):
return 'USE_BLUE'
else:
return 'USE_RED'
else:
// case 4.3.3
if A.topo_order < B.topo_order:
// case 4.3.3.1
if (alt_to_X == 'USE_BLUE'
and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
// case 4.3.3.2
if (alt_to_X == 'USE_RED'
and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
assert(False)
Figure 29: Select_Alternates_Proxy_Node()
Select_Alternates_Proxy_Node(P,F,primary_intf) determines whether it
is safe to use the blue path to P (which goes through X), the red
path to P (which goes through Y), or either, when the primary_intf to
node F (and possibly node F) fails. The basic approach is to run
Select_Alternates(X,F,primary_intf) and
Select_Alternates(Y,F,primary_intf) to determine which of the two MRT
paths to X and which of the two MRT paths to Y is safe to use in the
event of the failure of F. In general, we will find that if it is
safe to use a particular path to X or Y when F fails, and
Select_Proxy_Node_NHs() used that path when constructing the red or
blue path to reach P, then it will also be safe to use that path to
reach P when F fails. This rule has one exception which is covered
below. First, we give a concrete example of how
Select_Alternates_Proxy_Node() works in the common case.
The 21 ordering relationships used in Select_Proxy_Node_NHs() are
repeated in Select_Alternates_Proxy_Node(). We focus on case 4.1.1
to give a detailed example of the reasoning used in
Select_Alternates_Proxy_Node(). In Select_Proxy_Node_NHs(), we
determined for case 4.1.1 that the red next hops to X and the blue
next hops to Y allow us to reach X and Y by disjoint paths, and are
thus the blue and red next hops to reach P. Therefore, if
Select_Alternates(X, F, primary_intf) is run and we find that it is
safe to USE_RED to reach X, then we also conclude that it is safe to
use the MRT path through X to reach P (the blue path to P) when F
fails. Similarly, if we run Select_Alternates(Y, F, primary_intf)
and we find that it is safe to USE_BLUE to reach Y, then we also
conclude that it is safe to use the MRT path through Y to reach P
(the red path to P) when F fails. If both of the paths that were
used in Select_Proxy_Node_NHs() to construct the blue and red paths
to P are found to be safe to use to use to reach X and Y, t then we
conclude that we can use either the red or the blue path to P.
This simple reasoning gives the correct answer in most of the cases.
However, additional logic is needed when either A or B (but not both
A and B) is unordered with respect to S. This applies to cases
4.1.3, 4.2.3, 4.3.1, and 4.3.2. Looking at case 4.1.3 in more
detail, A is ordered less than S, but B is unordered with respect to
S. In the discussion of case 4.1.3 above, we saw that
Select_Proxy_Node_NHs() chose the red path to reach Y and the red
path to reach X. We also saw that the red path to reach Y will
follow the INCREASING next hops towards the localroot until it
reaches some node (L) which is ordered greater than B, after which it
will take DECREASING next hops to B. The problem is that the red
path to reach P (the one that goes through Y) won't necessarily be
the same as the red path to reach Y. This is because the next hop
that node L computes for its red next hop to reach P may be different
from the next hop it computes for its red next hop to reach Y. This
is because B is ordered lower than L, so L applies case 4.1.2 of
Select_Proxy_Node_NHs() in order to determine its next hops to reach
P. If A.topo_order<B.topo_order (case 4.1.2.1), then L will choose
DECREASING next hops directly to B, which is the same result that L
computes in Compute_MRT_NextHops() to reach Y. However, if
A.topo_order>B.topo_order (case 4.1.2.2), then L will choose
INCREASING next hops to reach B, which is different from what L
computes in Compute_MRT_NextHops() to reach Y. So, testing the
safety of the path for S to reach Y on failure of F as a surrogate
for the safety of using the red path to reach P is not reliable in
this case. It is possible construct topologies where the red path to
P hits F even though the red path to Y does not hit F.
Fortunately, there is enough information in the order relationships
that we have already computed to still figure out which alternate to
choose in these four cases. The basic idea is to always choose the
path involving the ordered node, unless that path would hit F.
Returning to case 4.1.3, we see that since A is ordered lower than S,
the only way for S to hit F using a simple DECREASING path to A is
for F to lie between A and S on the GADAG. This scenario is covered
by requiring that F be lower than S (but not also higher than S) and
that F.topo_order>A.topo_order in case 4.1.3.1.
We just need to confirm that it is safe to use the path involving B
in this scenario. In case 4.1.3.1, either F is between A and S on
the GADAG, or F is unordered with respect to A and lies on the
DECREASING path from S to the localroot. When F is between A and S
on the GADAG, then the path through B chosen to avoid A in
Select_Proxy_Node_NHs() will also avoid F. When F is unordered with
respect to A and lies on the DECREASING path from S to the localroot,
then we consider two cases. Either F.topo_order<B.topo_order or
F.topo_order>B.topo_order. In the first case, since
F.topo_order<B.topo_order and F.topo_order>A.topo_order, it must be
the case that A.topo_order<B.topo_order. Therefore, L will choose
DECREASING next hops directly to B (case 4.1.2.1), which cannot hit F
since F.topo_order<B.topo_order. In the second case, where
F.topo_order>B.topo_order, the only way for the path involving B to
hit F is if it DECREASES from L to B through F, i.e., it must be that
L>>F>>B. However, since S>>F, this would imply that S>>B. However,
we know that S is unordered with respect to B, so the second case
cannot occur. So we have demonstrated that the red path to P (which
goes via B and Y) is safe to use under the conditions of 4.1.3.1.
Similar reasoning can be applied to the other three special cases
where either A or B is unordered with respect to S.
6. MRT Lowpoint Algorithm: NextHop Conformance
This specification defines the MRT Lowpoint algorithm, which includes
the construction of a common GADAG and the computation of MRTRed and
MRTBlue next hops to each node in the graph. An implementation MAY
select any subset of next hops for MRTRed and MRTBlue that respect
the available nodes that are described in Section 5.7 for each of the
MRTRed and MRTBlue and the selected next hops are further along in
the interval of allowed nodes towards the destination.
For example, the MRTBlue next hops used when the destination Y >> X,
the computing router, MUST be one or more nodes, T, whose topo_order
is in the interval [X.topo_order, Y.topo_order] and where Y >> T or Y
is T. Similarly, the MRTRed next hops MUST be have a topo_order in
the interval [Rsmall.topo_order, X.topo_order] or [Y.topo_order,
Rbig.topo_order].
Implementations SHOULD implement the Select_Alternates() function to
pick an MRTFRR alternate.
7. Broadcast Interfaces
When broadcast interfaces are used to connect nodes, the broadcast
network MUST be represented as a pseudonode, where each real node
connects to the pseudonode. The interface metric in the direction
from real node to pseudonode is the nonzero interface metric, while
the interface metric in the direction from the pseudonode to the real
node is set to zero. This is consistent with the way that broadcast
interfaces are represented as pseudonodes in ISIS and OSPF.
Pseudonodes MUST be treated as equivalent to real nodes in the
network graph used in the MRT Lowpoint algorithm with a few
exceptions detailed below.
The pseudonodes MUST be included in the computation of the GADAG.
The neighbors of the pseudonode need to know the mrt_node_id of the
pseudonode in order to consistently order interfaces, which is needed
to compute the GADAG. The mrt_node_id for ISIS is the 7octet
neighbor system ID and pseudonode number in TLV 22 or TLV 222. The
mrt_node_id for OSPFv2 is the 4octet interface address of the
Designated Router found in the Link ID field for the link type 2
(transit network) in the RouterLSA. The mrt_node_id for OSPFv3 is
the 4 octet interface address of the Designated Router found in the
Neighbor Interface ID field for the link type 2 (transit network) in
the RouterLSA. Note that this is different from the Neighbor Router
ID field used for the mrt_node_id for pointtopoint links in OSPFv3
RouterLSAs given in Figure 15.
Pseudonodes MUST NOT be considered candidates for selection as GADAG
root. This rule is intended to result in a more stable networkwide
selection of GADAG root by removing the possibility that the change
of Designated Router or Designated Intermediate System on a broadcast
network can result in a change of GADAG root.
7.1. Computing MRT Next Hops on Broadcast Networks
The pseudonode does not correspond to a real node, so it is not
actually involved in forwarding. A real node on a broadcast network
cannot simply forward traffic to the broadcast network. It must
specify another real node on the broadcast network as the next hop.
On a network graph where a broadcast network is represented by a
pseudonode, this means that if a real node determines that the next
hop to reach a given destination is a pseudonode, it must also
determine the nextnexthop for that destination in the network
graph, which corresponds to a real node attached to the broadcast
network.
It is interesting to note that this issue is not unique to the MRT
algorithm, but is also encountered in normal SPF computations for
IGPs. Section 16.1.1 of [RFC2328] describes how this is done for
OSPF. When OSPF runs its shortestpath tree calculation, it deals
with pseudonodes in the following manner. Whenever the calculating
router finds a shorter path to reach a real destination node and the
shorter path to the destination is a single pseudonode hop, then the
next hop for that destination is taken from the interface IP address
in the RouterLSA correspond to the link to the real destination
node.
For ISIS, in the example pseudocode implementation of Dijkstra's
algorithm in Annex C of [ISO10589SecondEdition], whenever the
algorithm encounters an adjacency from a real node to a pseudonode,
it gets converted to a set of adjacencies from the real node to the
neighbors of the pseudonode. In this way, the computed next hops
point all the way to the real node, and not the pseudonode.
We could avoid the problem of determining next hops across
pseudonodes in MRT by converting the pseudonode representation of
broadcast networks to a full mesh of links between real nodes on the
same network. However, if we make that conversion before computing
the GADAG, we lose information about which links actually correspond
to a single physical interface into the broadcast network. This
could result computing red and blue next hops that use the same
broadcast interface, in which case neither the red nor the blue next
hop would be usable as an alternate on failure of the broadcast
interface.
Instead, we take the following approach, which maintains the property
that either the red and blue next hop will avoid the broadcast
network, if topologically allowed. We run the MRT Lowpoint algorithm
treating the pseudonodes as equivalent to real nodes in the network
graph, with the exceptions noted above. In addition to running the
MRT Lowpoint algorithm from the point of view of itself, a computing
router connected to a pseudonode MUST also run the MRT Lowpoint
algorithm from the point of view of each of its pseudonode neighbors.
For example, if a computing router S determines that its MRT red next
hop to reach a destination D is a pseudonode P, S looks at its MRT
Lowpoint algorithm computation from P's point of view to determine
P's red next hop to reach D, say interface 1 on node X. S now knows
that its real red next hop to reach D is interface 1 on node X on the
broadcast network represented by P, and it can install the
corresponding entry in its FIB.
7.2. Using MRT Next Hops as Alternates in the Event of Failures on
Broadcast Networks
In the previous section, we specified how to compute MRT next hops
when broadcast networks are involved. In this section, we discuss
how a PLR can use those MRT next hops in the event of failures
involving broadcast networks.
A PLR attached to a broadcast network running only OSPF or ISIS with
large Hello intervals has limited ability to quickly detect failures
on a broadcast network. The only failure mode that can be quickly
detected is the failure of the physical interface connecting the PLR
to the broadcast network. For the failure of the interface
connecting the PLR to the broadcast network, the alternate that
avoids the broadcast network can be computed by using the broadcast
network pseudonode as F, the primary nexthop node, in
Select_Alternates(). This will choose an alternate path that avoids
the broadcast network. However, the alternate path will not
necessarily avoid all of the real nodes connected to the broadcast
network. This is because we have used the pseudonode to represent
the broadcast network. And we have enforced the nodeprotecting
property of MRT on the pseudonode to provide protection against
failure of the broadcast network, not the real nexthop nodes on the
broadcast network. This is the best that we can hope to do if
failure of the broadcast interface is the only failure mode that the
PLR can respond to.
We can improve on this if the PLR also has the ability to quickly
detect a lack of connectivity across the broadcast network to a given
IPlayer node. This can be accomplished by running BFD between all
pairs of IGP neighbors on the broadcast network. Note that in the
case of OSPF, this would require establishing BFD sessions between
all pairs of neighbors in the 2WAY state. When the PLR can quickly
detect the failure of a particular next hop across a broadcast
network, the PLR can be more selective in its choice of alternates.
For example, when the PLR observes that connectivity to an IPlayer
node on a broadcast network has failed, the PLR may choose to still
use the broadcast network to reach other IPlayer nodes that are
still reachable. Or, if the PLR observes that connectivity has
failed to several IPlayer nodes on the same broadcast network, it
may choose to treat the entire broadcast network as failed. The
choice of MRT alternates by a PLR for a particular set of failure
conditions is a local decision, since it does not require
coordination with other nodes.
8. Evaluation of Alternative Methods for Constructing GADAGs
This document specifies the MRT Lowpoint algorithm. One component of
the algorithm involves constructing a common GADAG based on the
network topology. The MRT Lowpoint algorithm computes the GADAG
using the method described in Section 5.5. This method aims to
minimize the amount of computation required to compute the GADAG. In
the process of developing the MRT Lowpoint algorithm, two alternative
methods for constructing GADAGs were also considered. These
alternative methods are described in Appendices B and C. In general,
these other two methods require more computation to compute the
GADAG. The analysis below was performed to determine if the
alternative GADAG construction methods produce shorter MRT alternate
paths in real network topologies, and if so, to what extent.
Figure 30 compares results obtained using the three different methods
for constructing GADAGs on five different service provider network
topologies. MRT_LOWPOINT indicates the method specified in
Section 5.5, while MRT_SPF and MRT_HYBRID indicate the methods
specified in Appendices B and C, respectively. The columns on the
right present the distribution of alternate path lengths for each
GADAG construction method. Each MRT computation was performed using
a same GADAG root chosen based on centrality.
For three of the topologies analyzed (T201, T206, and T211), the use
of MRT_SPF or MRT_HYBRID methods does not appear to provide a
significantly shorter alternate path lengths compared to the
MRT_LOWPOINT method. However, for two of the topologies (T216 and
T219), the use of the MRT_SPF method resulted in noticeably shorter
alternate path lengths than the use of the MRT_LOWPOINT or MRT_HYBRID
methods.
It was decided to use the MRT_LOWPOINT method to construct the GADAG
in the algorithm specified in this document, in order to initially
offer an algorithm with lower computational requirements. These
results indicate that in the future it may be useful to evaluate and
potentially specify other MRT Lowpoint algorithm variants that use
different GADAG construction methods.
++
 Topology name  percentage of failure scenarios 
  protected by an alternate N hops 
 GADAG construction  longer than the primary path 
 method ++
          no 
      10 12 14  alt
 0123456789111315 <16
+++++++++++
 T201(avg primary hops=3.5)          
 MRT_HYBRID  33 26 23 6 3    
 MRT_SPF  33 36 23 6 3    
 MRT_LOWPOINT  33 36 23 6 3    
+++++++++++
 T206(avg primary hops=3.7)          
 MRT_HYBRID  50 35 13 2     
 MRT_SPF  50 35 13 2     
 MRT_LOWPOINT  55 32 13      
+++++++++++
 T211(avg primary hops=3.3)          
 MRT_HYBRID  86 14       
 MRT_SPF  86 14       
 MRT_LOWPOINT  85 15 1      
+++++++++++
 T216(avg primary hops=5.2)          
 MRT_HYBRID  23 22 18 13 10 7 4 2 2
 MRT_SPF  35 32 19 9 3 1   
 MRT_LOWPOINT  28 25 18 11 7 6 3 2 1
+++++++++++
 T219(avg primary hops=7.7)          
 MRT_HYBRID  20 16 13 10 7 5 5 5 3
 MRT_SPF  31 23 19 12 7 4 2 1 
 MRT_LOWPOINT  19 14 15 12 10 8 7 6 10
+++++++++++
Figure 30: The Length of Alternate Paths for Various GADAG
Construction Methods
9. Operational Considerations
This section discusses operational considerations related to the MRT
Lowpoint algorithm and other potential MRT algorithm variants. For a
discussion of operational considerations related to MRTFRR in
general, see the "Operational Considerations" section of [RFC7812].
9.1. GADAG Root Selection
The Default MRT Profile uses the GADAG Root Selection Priority
advertised by routers as the primary criterion for selecting the
GADAG root. It is RECOMMENDED that an operator designate a set of
routers as good choices for selection as GADAG root by setting the
GADAG Root Selection Priority for that set of routers to lower (more
preferred) numerical values. Criteria for making this designation
are discussed below.
Analysis has shown that the centrality of a router can have a
significant impact on the lengths of the alternate paths computed.
Therefore, it is RECOMMENDED that offline analysis that considers
the centrality of a router be used to help determine how good a
choice a particular router is for the role of GADAG root.
If the router currently selected as GADAG root becomes unreachable in
the IGP topology, then a new GADAG root will be selected. Changing
the GADAG root can change the overall structure of the GADAG as well
the paths of the red and MRTBlue trees built using that GADAG. In
order to minimize change in the associated red and MRTBlue
forwarding entries that can result from changing the GADAG root, it
is RECOMMENDED that operators prioritize for selection as GADAG root
those routers that are expected to consistently remain part of the
IGP topology.
9.2. DestinationRooted GADAGs
The MRT Lowpoint algorithm constructs a single GADAG rooted at a
single node selected as the GADAG root. It is also possible to
construct a different GADAG for each destination, with the GADAG
rooted at the destination. A router can compute the MRTRed and MRT
Blue next hops for that destination based on the GADAG rooted at that
destination. Building a different GADAG for each destination is
computationally more expensive, but it may give somewhat shorter
alternate paths. Using destinationrooted GADAGs would require a new
MRT profile to be created with a new MRT algorithm specification,
since all routers in the MRT Island would need to use destination
rooted GADAGs.
10. Security Considerations
The algorithm described in this document does not introduce new
security concerns beyond those already discussed in the document
describing the MRT FRR architecture [RFC7812].
11. References
11.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<http://www.rfceditor.org/info/rfc2119>.
[RFC7812] Atlas, A., Bowers, C., and G. Enyedi, "An Architecture for
IP/LDP Fast Reroute Using Maximally Redundant Trees
(MRTFRR)", RFC 7812, DOI 10.17487/RFC7812, June 2016,
<http://www.rfceditor.org/info/rfc7812>.
11.2. Informative References
[EnyediThesis]
Enyedi, G., "Novel Algorithms for IP Fast Reroute",
Department of Telecommunications and Media Informatics,
Budapest University of Technology and Economics Ph.D.
Thesis, February 2011,
<https://repozitorium.omikk.bme.hu/bitstream/
handle/10890/1040/ertekezes.pdf>.
[IEEE8021Qca]
IEEE, "IEEE Standard for Local and metropolitan area
networks  Bridges and Bridged Networks  Amendment 24:
Path Control and Reservation", IEEE 802.1Qca2015,
DOI 10.1109/IEEESTD.2016.7434544, 2016,
<https://standards.ieee.org/findstds/
standard/802.1Qca2015.html>.
[ISO10589SecondEdition]
International Organization for Standardization,
"Intermediate system to Intermediate system intradomain
routeing information exchange protocol for use in
conjunction with the protocol for providing the
connectionlessmode Network Service (ISO 8473)", ISO/
IEC 10589:2002, Second Edition, November 2002.
[Kahn_1962_topo_sort]
Kahn, A., "Topological sorting of large networks",
Communications of the ACM, Volume 5, Issue 11 DOI
10.1145/368996.369025, November 1962,
<http://dl.acm.org/citation.cfm?doid=368996.369025>.
[MRTLinear]
Enyedi, G., Retvari, G., and A. Csaszar, "On Finding
Maximally Redundant Trees in Strictly Linear Time", IEEE
Symposium on Computers and Communications (ISCC), 2009,
<http://opti.tmit.bme.hu/~enyedi/ipfrr/
distMaxRedTree.pdf>.
[RFC2328] Moy, J., "OSPF Version 2", STD 54, RFC 2328,
DOI 10.17487/RFC2328, April 1998,
<http://www.rfceditor.org/info/rfc2328>.
Appendix A. Python Implementation of MRT Lowpoint Algorithm
Below is Python code implementing the MRT Lowpoint algorithm
specified in this document. The code is also posted on GitHub
<https://github.com/cbowers/draftietfrtgwgmrtfrr
algorithm/blob/python_code_RFC7811/src/mrt_lowpoint_draft_text.py>.
While this Python code is believed to correctly implement the
pseudocode description of the algorithm, in the event of a
difference, the pseudocode description should be considered
normative.
<CODE BEGINS>
# This program has been tested to run on Python 2.6 and 2.7
# (specifically Python 2.6.6 and 2.7.8 were tested).
# The program has known incompatibilities with Python 3.X.
# When executed, this program will generate a text file describing
# an example topology. It then reads that text file back in as input
# to create the example topology, and runs the MRT Lowpoint algorithm.
# This was done to simplify the inclusion of the program as a single
# text file that can be extracted from the RFC.
# The output of the program is four text files containing a description
# of the GADAG, the blue and MRTReds for all destinations, and the
# MRT alternates for all failures.
import random
import os.path
import heapq
# simple Class definitions allow structurelike dot notation for
# variables and a convenient place to initialize those variables.
class Topology:
def __init__(self):
self.gadag_root = None
self.node_list = []
self.node_dict = {}
self.test_gr = None
self.island_node_list_for_test_gr = []
self.stored_named_proxy_dict = {}
self.init_new_computing_router()
def init_new_computing_router(self):
self.island_node_list = []
self.named_proxy_dict = {}
class Node:
def __init__(self):
self.node_id = None
self.intf_list = []
self.profile_id_list = [0]
self.GR_sel_priority = 128
self.blue_next_hops_dict = {}
self.red_next_hops_dict = {}
self.blue_to_green_nh_dict = {}
self.red_to_green_nh_dict = {}
self.prefix_cost_dict = {}
self.pnh_dict = {}
self.alt_dict = {}
self.init_new_computing_router()
def init_new_computing_router(self):
self.island_intf_list = []
self.IN_MRT_ISLAND = False
self.IN_GADAG = False
self.dfs_number = None
self.dfs_parent = None
self.dfs_parent_intf = None
self.dfs_child_list = []
self.lowpoint_number = None
self.lowpoint_parent = None
self.lowpoint_parent_intf = None
self.localroot = None
self.block_id = None
self.IS_CUT_VERTEX = False
self.blue_next_hops = []
self.red_next_hops = []
self.primary_next_hops = []
self.alt_list = []
class Interface:
def __init__(self):
self.metric = None
self.area = None
self.MRT_INELIGIBLE = False
self.IGP_EXCLUDED = False
self.SIMULATION_OUTGOING = False
self.init_new_computing_router()
def init_new_computing_router(self):
self.UNDIRECTED = True
self.INCOMING = False
self.OUTGOING = False
self.INCOMING_STORED = False
self.OUTGOING_STORED = False
self.IN_MRT_ISLAND = False
self.PROCESSED = False
class Bundle:
def __init__(self):
self.UNDIRECTED = True
self.OUTGOING = False
self.INCOMING = False
class Alternate:
def __init__(self):
self.failed_intf = None
self.red_or_blue = None
self.nh_list = []
self.fec = 'NO_ALTERNATE'
self.prot = 'NO_PROTECTION'
self.info = 'NONE'
class Proxy_Node_Attachment_Router:
def __init__(self):
self.prefix = None
self.node = None
self.named_proxy_cost = None
self.min_lfin = None
self.nh_intf_list = []
class Named_Proxy_Node:
def __init__(self):
self.node_id = None #this is the prefix_id
self.node_prefix_cost_list = []
self.lfin_list = []
self.pnar1 = None
self.pnar2 = None
self.pnar_X = None
self.pnar_Y = None
self.blue_next_hops = []
self.red_next_hops = []
self.primary_next_hops = []
self.blue_next_hops_dict = {}
self.red_next_hops_dict = {}
self.pnh_dict = {}
self.alt_dict = {}
def Interface_Compare(intf_a, intf_b):
if intf_a.metric < intf_b.metric:
return 1
if intf_b.metric < intf_a.metric:
return 1
if intf_a.remote_node.node_id < intf_b.remote_node.node_id:
return 1
if intf_b.remote_node.node_id < intf_a.remote_node.node_id:
return 1
return 0
def Sort_Interfaces(topo):
for node in topo.island_node_list:
node.island_intf_list.sort(Interface_Compare)
def Reset_Computed_Node_and_Intf_Values(topo):
topo.init_new_computing_router()
for node in topo.node_list:
node.init_new_computing_router()
for intf in node.intf_list:
intf.init_new_computing_router()
# This function takes a file with links represented by 2digit
# numbers in the format:
# 01,05,10
# 05,02,30
# 02,01,15
# which represents a triangle topology with nodes 01, 05, and 02
# and symmetric metrics of 10, 30, and 15.
# Inclusion of a fourth column makes the metrics for the link
# asymmetric. An entry of:
# 02,07,10,15
# creates a link from node 02 to 07 with metrics 10 and 15.
def Create_Topology_From_File(filename):
topo = Topology()
node_id_set= set()
cols_list = []
# on first pass just create nodes
with open(filename + '.csv') as topo_file:
for line in topo_file:
line = line.rstrip('\r\n')
cols=line.split(',')
cols_list.append(cols)
nodea_node_id = int(cols[0])
nodeb_node_id = int(cols[1])
if (nodea_node_id > 999 or nodeb_node_id > 999):
print("node_id must be between 0 and 999.")
print("exiting.")
exit()
node_id_set.add(nodea_node_id)
node_id_set.add(nodeb_node_id)
for node_id in node_id_set:
node = Node()
node.node_id = node_id
topo.node_list.append(node)
topo.node_dict[node_id] = node
# on second pass create interfaces
for cols in cols_list:
nodea_node_id = int(cols[0])
nodeb_node_id = int(cols[1])
metric = int(cols[2])
reverse_metric = int(cols[2])
if len(cols) > 3:
reverse_metric=int(cols[3])
nodea = topo.node_dict[nodea_node_id]
nodeb = topo.node_dict[nodeb_node_id]
nodea_intf = Interface()
nodea_intf.metric = metric
nodea_intf.area = 0
nodeb_intf = Interface()
nodeb_intf.metric = reverse_metric
nodeb_intf.area = 0
nodea_intf.remote_intf = nodeb_intf
nodeb_intf.remote_intf = nodea_intf
nodea_intf.remote_node = nodeb
nodeb_intf.remote_node = nodea
nodea_intf.local_node = nodea
nodeb_intf.local_node = nodeb
nodea_intf.link_data = len(nodea.intf_list)
nodeb_intf.link_data = len(nodeb.intf_list)
nodea.intf_list.append(nodea_intf)
nodeb.intf_list.append(nodeb_intf)
return topo
def MRT_Island_Identification(topo, computing_rtr, profile_id, area):
if profile_id in computing_rtr.profile_id_list:
computing_rtr.IN_MRT_ISLAND = True
explore_list = [computing_rtr]
else:
return
while explore_list != []:
next_rtr = explore_list.pop()
for intf in next_rtr.intf_list:
if ( (not intf.IN_MRT_ISLAND)
and (not intf.MRT_INELIGIBLE)
and (not intf.remote_intf.MRT_INELIGIBLE)
and (not intf.IGP_EXCLUDED) and intf.area == area
and (profile_id in intf.remote_node.profile_id_list)):
intf.IN_MRT_ISLAND = True
intf.remote_intf.IN_MRT_ISLAND = True
if (not intf.remote_node.IN_MRT_ISLAND):
intf.remote_INTF.IN_MRT_ISLAND = True
explore_list.append(intf.remote_node)
def Compute_Island_Node_List_For_Test_GR(topo, test_gr):
Reset_Computed_Node_and_Intf_Values(topo)
topo.test_gr = topo.node_dict[test_gr]
MRT_Island_Identification(topo, topo.test_gr, 0, 0)
for node in topo.node_list:
if node.IN_MRT_ISLAND:
topo.island_node_list_for_test_gr.append(node)
def Set_Island_Intf_and_Node_Lists(topo):
for node in topo.node_list:
if node.IN_MRT_ISLAND:
topo.island_node_list.append(node)
for intf in node.intf_list:
if intf.IN_MRT_ISLAND:
node.island_intf_list.append(intf)
global_dfs_number = None
def Lowpoint_Visit(x, parent, intf_p_to_x):
global global_dfs_number
x.dfs_number = global_dfs_number
x.lowpoint_number = x.dfs_number
global_dfs_number += 1
x.dfs_parent = parent
if intf_p_to_x == None:
x.dfs_parent_intf = None
else:
x.dfs_parent_intf = intf_p_to_x.remote_intf
x.lowpoint_parent = None
if parent != None:
parent.dfs_child_list.append(x)
for intf in x.island_intf_list:
if intf.remote_node.dfs_number == None:
Lowpoint_Visit(intf.remote_node, x, intf)
if intf.remote_node.lowpoint_number < x.lowpoint_number:
x.lowpoint_number = intf.remote_node.lowpoint_number
x.lowpoint_parent = intf.remote_node
x.lowpoint_parent_intf = intf
else:
if intf.remote_node is not parent:
if intf.remote_node.dfs_number < x.lowpoint_number:
x.lowpoint_number = intf.remote_node.dfs_number
x.lowpoint_parent = intf.remote_node
x.lowpoint_parent_intf = intf
def Run_Lowpoint(topo):
global global_dfs_number
global_dfs_number = 0
Lowpoint_Visit(topo.gadag_root, None, None)
max_block_id = None
def Assign_Block_ID(x, cur_block_id):
global max_block_id
x.block_id = cur_block_id
for c in x.dfs_child_list:
if (c.localroot is x):
max_block_id += 1
Assign_Block_ID(c, max_block_id)
else:
Assign_Block_ID(c, cur_block_id)
def Run_Assign_Block_ID(topo):
global max_block_id
max_block_id = 0
Assign_Block_ID(topo.gadag_root, max_block_id)
def Construct_Ear(x, stack, intf, ear_type):
ear_list = []
cur_intf = intf
not_done = True
while not_done:
cur_intf.UNDIRECTED = False
cur_intf.OUTGOING = True
cur_intf.remote_intf.UNDIRECTED = False
cur_intf.remote_intf.INCOMING = True
if cur_intf.remote_node.IN_GADAG == False:
cur_intf.remote_node.IN_GADAG = True
ear_list.append(cur_intf.remote_node)
if ear_type == 'CHILD':
cur_intf = cur_intf.remote_node.lowpoint_parent_intf
else:
assert ear_type == 'NEIGHBOR'
cur_intf = cur_intf.remote_node.dfs_parent_intf
else:
not_done = False
if ear_type == 'CHILD' and cur_intf.remote_node is x:
# x is a cutvertex and the local root for the block
# in which the ear is computed
x.IS_CUT_VERTEX = True
localroot = x
else:
# inherit local root from the end of the ear
localroot = cur_intf.remote_node.localroot
while ear_list != []:
y = ear_list.pop()
y.localroot = localroot
stack.append(y)
def Construct_GADAG_via_Lowpoint(topo):
gadag_root = topo.gadag_root
gadag_root.IN_GADAG = True
gadag_root.localroot = None
stack = []
stack.append(gadag_root)
while stack != []:
x = stack.pop()
for intf in x.island_intf_list:
if ( intf.remote_node.IN_GADAG == False
and intf.remote_node.dfs_parent is x ):
Construct_Ear(x, stack, intf, 'CHILD' )
for intf in x.island_intf_list:
if (intf.remote_node.IN_GADAG == False
and intf.remote_node.dfs_parent is not x):
Construct_Ear(x, stack, intf, 'NEIGHBOR')
def Assign_Remaining_Lowpoint_Parents(topo):
for node in topo.island_node_list:
if ( node is not topo.gadag_root
and node.lowpoint_parent == None ):
node.lowpoint_parent = node.dfs_parent
node.lowpoint_parent_intf = node.dfs_parent_intf
node.lowpoint_number = node.dfs_parent.dfs_number
def Add_Undirected_Block_Root_Links(topo):
for node in topo.island_node_list:
if node.IS_CUT_VERTEX or node is topo.gadag_root:
for intf in node.island_intf_list:
if ( intf.remote_node.localroot is not node
or intf.PROCESSED ):
continue
bundle_list = []
bundle = Bundle()
for intf2 in node.island_intf_list:
if intf2.remote_node is intf.remote_node:
bundle_list.append(intf2)
if not intf2.UNDIRECTED:
bundle.UNDIRECTED = False
if intf2.INCOMING:
bundle.INCOMING = True
if intf2.OUTGOING:
bundle.OUTGOING = True
if bundle.UNDIRECTED:
for intf3 in bundle_list:
intf3.UNDIRECTED = False
intf3.remote_intf.UNDIRECTED = False
intf3.PROCESSED = True
intf3.remote_intf.PROCESSED = True
intf3.OUTGOING = True
intf3.remote_intf.INCOMING = True
else:
if (bundle.OUTGOING and bundle.INCOMING):
for intf3 in bundle_list:
intf3.UNDIRECTED = False
intf3.remote_intf.UNDIRECTED = False
intf3.PROCESSED = True
intf3.remote_intf.PROCESSED = True
intf3.OUTGOING = True
intf3.INCOMING = True
intf3.remote_intf.INCOMING = True
intf3.remote_intf.OUTGOING = True
elif bundle.OUTGOING:
for intf3 in bundle_list:
intf3.UNDIRECTED = False
intf3.remote_intf.UNDIRECTED = False
intf3.PROCESSED = True
intf3.remote_intf.PROCESSED = True
intf3.OUTGOING = True
intf3.remote_intf.INCOMING = True
elif bundle.INCOMING:
for intf3 in bundle_list:
intf3.UNDIRECTED = False
intf3.remote_intf.UNDIRECTED = False
intf3.PROCESSED = True
intf3.remote_intf.PROCESSED = True
intf3.INCOMING = True
intf3.remote_intf.OUTGOING = True
def Modify_Block_Root_Incoming_Links(topo):
for node in topo.island_node_list:
if ( node.IS_CUT_VERTEX == True or node is topo.gadag_root ):
for intf in node.island_intf_list:
if intf.remote_node.localroot is node:
if intf.INCOMING:
intf.INCOMING = False
intf.INCOMING_STORED = True
intf.remote_intf.OUTGOING = False
intf.remote_intf.OUTGOING_STORED = True
def Revert_Block_Root_Incoming_Links(topo):
for node in topo.island_node_list:
if ( node.IS_CUT_VERTEX == True or node is topo.gadag_root ):
for intf in node.island_intf_list:
if intf.remote_node.localroot is node:
if intf.INCOMING_STORED:
intf.INCOMING = True
intf.remote_intf.OUTGOING = True
intf.INCOMING_STORED = False
intf.remote_intf.OUTGOING_STORED = False
def Run_Topological_Sort_GADAG(topo):
Modify_Block_Root_Incoming_Links(topo)
for node in topo.island_node_list:
node.unvisited = 0
for intf in node.island_intf_list:
if (intf.INCOMING == True):
node.unvisited += 1
working_list = []
topo_order_list = []
working_list.append(topo.gadag_root)
while working_list != []:
y = working_list.pop(0)
topo_order_list.append(y)
for intf in y.island_intf_list:
if ( intf.OUTGOING == True):
intf.remote_node.unvisited = 1
if intf.remote_node.unvisited == 0:
working_list.append(intf.remote_node)
next_topo_order = 1
while topo_order_list != []:
y = topo_order_list.pop(0)
y.topo_order = next_topo_order
next_topo_order += 1
Revert_Block_Root_Incoming_Links(topo)
def Set_Other_Undirected_Links_Based_On_Topo_Order(topo):
for node in topo.island_node_list:
for intf in node.island_intf_list:
if intf.UNDIRECTED:
if node.topo_order < intf.remote_node.topo_order:
intf.OUTGOING = True
intf.UNDIRECTED = False
intf.remote_intf.INCOMING = True
intf.remote_intf.UNDIRECTED = False
else:
intf.INCOMING = True
intf.UNDIRECTED = False
intf.remote_intf.OUTGOING = True
intf.remote_intf.UNDIRECTED = False
def Initialize_Temporary_Interface_Flags(topo):
for node in topo.island_node_list:
for intf in node.island_intf_list:
intf.PROCESSED = False
intf.INCOMING_STORED = False
intf.OUTGOING_STORED = False
def Add_Undirected_Links(topo):
Initialize_Temporary_Interface_Flags(topo)
Add_Undirected_Block_Root_Links(topo)
Run_Topological_Sort_GADAG(topo)
Set_Other_Undirected_Links_Based_On_Topo_Order(topo)
def In_Common_Block(x,y):
if ( (x.block_id == y.block_id)
or ( x is y.localroot) or (y is x.localroot) ):
return True
return False
def Copy_List_Items(target_list, source_list):
del target_list[:] # Python idiom to remove all elements of a list
for element in source_list:
target_list.append(element)
def Add_Item_To_List_If_New(target_list, item):
if item not in target_list:
target_list.append(item)
def Store_Results(y, direction):
if direction == 'INCREASING':
y.HIGHER = True
Copy_List_Items(y.blue_next_hops, y.next_hops)
if direction == 'DECREASING':
y.LOWER = True
Copy_List_Items(y.red_next_hops, y.next_hops)
if direction == 'NORMAL_SPF':
y.primary_spf_metric = y.spf_metric
Copy_List_Items(y.primary_next_hops, y.next_hops)
if direction == 'MRT_ISLAND_SPF':
Copy_List_Items(y.mrt_island_next_hops, y.next_hops)
if direction == 'COLLAPSED_SPF':
y.collapsed_metric = y.spf_metric
Copy_List_Items(y.collapsed_next_hops, y.next_hops)
# Note that the Python heapq function allows for duplicate items,
# so we use the 'spf_visited' property to only consider a node
# as min_node the first time it gets removed from the heap.
def SPF_No_Traverse_Block_Root(topo, spf_root, block_root, direction):
spf_heap = []
for y in topo.island_node_list:
y.spf_metric = 2147483647 # 2^311
y.next_hops = []
y.spf_visited = False
spf_root.spf_metric = 0
heapq.heappush(spf_heap,
(spf_root.spf_metric, spf_root.node_id, spf_root) )
while spf_heap != []:
#extract third element of tuple popped from heap
min_node = heapq.heappop(spf_heap)[2]
if min_node.spf_visited:
continue
min_node.spf_visited = True
Store_Results(min_node, direction)
if ( (min_node is spf_root) or (min_node is not block_root) ):
for intf in min_node.island_intf_list:
if ( ( (direction == 'INCREASING' and intf.OUTGOING )
or (direction == 'DECREASING' and intf.INCOMING ) )
and In_Common_Block(spf_root, intf.remote_node) ) :
path_metric = min_node.spf_metric + intf.metric
if path_metric < intf.remote_node.spf_metric:
intf.remote_node.spf_metric = path_metric
if min_node is spf_root:
intf.remote_node.next_hops = [intf]
else:
Copy_List_Items(intf.remote_node.next_hops,
min_node.next_hops)
heapq.heappush(spf_heap,
( intf.remote_node.spf_metric,
intf.remote_node.node_id,
intf.remote_node ) )
elif path_metric == intf.remote_node.spf_metric:
if min_node is spf_root:
Add_Item_To_List_If_New(
intf.remote_node.next_hops,intf)
else:
for nh_intf in min_node.next_hops:
Add_Item_To_List_If_New(
intf.remote_node.next_hops,nh_intf)
def Normal_SPF(topo, spf_root):
spf_heap = []
for y in topo.node_list:
y.spf_metric = 2147483647 # 2^311 as max metric
y.next_hops = []
y.primary_spf_metric = 2147483647
y.primary_next_hops = []
y.spf_visited = False
spf_root.spf_metric = 0
heapq.heappush(spf_heap,
(spf_root.spf_metric,spf_root.node_id,spf_root) )
while spf_heap != []:
#extract third element of tuple popped from heap
min_node = heapq.heappop(spf_heap)[2]
if min_node.spf_visited:
continue
min_node.spf_visited = True
Store_Results(min_node, 'NORMAL_SPF')
for intf in min_node.intf_list:
path_metric = min_node.spf_metric + intf.metric
if path_metric < intf.remote_node.spf_metric:
intf.remote_node.spf_metric = path_metric
if min_node is spf_root:
intf.remote_node.next_hops = [intf]
else:
Copy_List_Items(intf.remote_node.next_hops,
min_node.next_hops)
heapq.heappush(spf_heap,
( intf.remote_node.spf_metric,
intf.remote_node.node_id,
intf.remote_node ) )
elif path_metric == intf.remote_node.spf_metric:
if min_node is spf_root:
Add_Item_To_List_If_New(
intf.remote_node.next_hops,intf)
else:
for nh_intf in min_node.next_hops:
Add_Item_To_List_If_New(
intf.remote_node.next_hops,nh_intf)
def Set_Edge(y):
if (y.blue_next_hops == [] and y.red_next_hops == []):
Set_Edge(y.localroot)
Copy_List_Items(y.blue_next_hops,y.localroot.blue_next_hops)
Copy_List_Items(y.red_next_hops ,y.localroot.red_next_hops)
y.order_proxy = y.localroot.order_proxy
def Compute_MRT_NH_For_One_Src_To_Island_Dests(topo,x):
for y in topo.island_node_list:
y.HIGHER = False
y.LOWER = False
y.red_next_hops = []
y.blue_next_hops = []
y.order_proxy = y
SPF_No_Traverse_Block_Root(topo, x, x.localroot, 'INCREASING')
SPF_No_Traverse_Block_Root(topo, x, x.localroot, 'DECREASING')
for y in topo.island_node_list:
if ( y is not x and (y.block_id == x.block_id) ):
assert (not ( y is x.localroot or x is y.localroot) )
assert(not (y.HIGHER and y.LOWER) )
if y.HIGHER == True:
Copy_List_Items(y.red_next_hops,
x.localroot.red_next_hops)
elif y.LOWER == True:
Copy_List_Items(y.blue_next_hops,
x.localroot.blue_next_hops)
else:
Copy_List_Items(y.blue_next_hops,
x.localroot.red_next_hops)
Copy_List_Items(y.red_next_hops,
x.localroot.blue_next_hops)
# Inherit x's MRT next hops to reach the GADAG root
# from x's MRT next hops to reach its local root,
# but first check if x is the gadag_root (in which case
# x does not have a local root) or if x's local root
# is the gadag root (in which case we already have the
# x's MRT next hops to reach the gadag root)
if x is not topo.gadag_root and x.localroot is not topo.gadag_root:
Copy_List_Items(topo.gadag_root.blue_next_hops,
x.localroot.blue_next_hops)
Copy_List_Items(topo.gadag_root.red_next_hops,
x.localroot.red_next_hops)
topo.gadag_root.order_proxy = x.localroot
# Inherit next hops and order_proxies to other blocks
for y in topo.island_node_list:
if (y is not topo.gadag_root and y is not x ):
Set_Edge(y)
def Store_MRT_Nexthops_For_One_Src_To_Island_Dests(topo,x):
for y in topo.island_node_list:
if y is x:
continue
x.blue_next_hops_dict[y.node_id] = []
x.red_next_hops_dict[y.node_id] = []
Copy_List_Items(x.blue_next_hops_dict[y.node_id],
y.blue_next_hops)
Copy_List_Items(x.red_next_hops_dict[y.node_id],
y.red_next_hops)
def Store_Primary_and_Alts_For_One_Src_To_Island_Dests(topo,x):
for y in topo.island_node_list:
x.pnh_dict[y.node_id] = []
Copy_List_Items(x.pnh_dict[y.node_id], y.primary_next_hops)
x.alt_dict[y.node_id] = []
Copy_List_Items(x.alt_dict[y.node_id], y.alt_list)
def Store_Primary_NHs_For_One_Source_To_Nodes(topo,x):
for y in topo.node_list:
x.pnh_dict[y.node_id] = []
Copy_List_Items(x.pnh_dict[y.node_id], y.primary_next_hops)
def Store_MRT_NHs_For_One_Src_To_Named_Proxy_Nodes(topo,x):
for prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
x.blue_next_hops_dict[P.node_id] = []
x.red_next_hops_dict[P.node_id] = []
Copy_List_Items(x.blue_next_hops_dict[P.node_id],
P.blue_next_hops)
Copy_List_Items(x.red_next_hops_dict[P.node_id],
P.red_next_hops)
def Store_Alts_For_One_Src_To_Named_Proxy_Nodes(topo,x):
for prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
x.alt_dict[P.node_id] = []
Copy_List_Items(x.alt_dict[P.node_id],
P.alt_list)
def Store_Primary_NHs_For_One_Src_To_Named_Proxy_Nodes(topo,x):
for prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
x.pnh_dict[P.node_id] = []
Copy_List_Items(x.pnh_dict[P.node_id],
P.primary_next_hops)
def Select_Alternates_Internal(D, F, primary_intf,
D_lower, D_higher, D_topo_order):
if D_higher and D_lower:
if F.HIGHER and F.LOWER:
if F.topo_order > D_topo_order:
return 'USE_BLUE'
else:
return 'USE_RED'
if F.HIGHER:
return 'USE_RED'
if F.LOWER:
return 'USE_BLUE'
assert(primary_intf.MRT_INELIGIBLE
or primary_intf.remote_intf.MRT_INELIGIBLE)
return 'USE_RED_OR_BLUE'
if D_higher:
if F.HIGHER and F.LOWER:
return 'USE_BLUE'
if F.LOWER:
return 'USE_BLUE'
if F.HIGHER:
if (F.topo_order > D_topo_order):
return 'USE_BLUE'
if (F.topo_order < D_topo_order):
return 'USE_RED'
assert(False)
assert(primary_intf.MRT_INELIGIBLE
or primary_intf.remote_intf.MRT_INELIGIBLE)
return 'USE_RED_OR_BLUE'
if D_lower:
if F.HIGHER and F.LOWER:
return 'USE_RED'
if F.HIGHER:
return 'USE_RED'
if F.LOWER:
if F.topo_order > D_topo_order:
return 'USE_BLUE'
if F.topo_order < D_topo_order:
return 'USE_RED'
assert(False)
assert(primary_intf.MRT_INELIGIBLE
or primary_intf.remote_intf.MRT_INELIGIBLE)
return 'USE_RED_OR_BLUE'
else: # D is unordered wrt S
if F.HIGHER and F.LOWER:
if primary_intf.OUTGOING and primary_intf.INCOMING:
# This can happen when F and D are in different blocks
return 'USE_RED_OR_BLUE'
if primary_intf.OUTGOING:
return 'USE_BLUE'
if primary_intf.INCOMING:
return 'USE_RED'
#This can occur when primary_intf is MRT_INELIGIBLE.
#This appears to be a case where the special
#construction of the GADAG allows us to choose red,
#whereas with an arbitrary GADAG, neither red nor blue
#is guaranteed to work.
assert(primary_intf.MRT_INELIGIBLE
or primary_intf.remote_intf.MRT_INELIGIBLE)
return 'USE_RED'
if F.LOWER:
return 'USE_RED'
if F.HIGHER:
return 'USE_BLUE'
assert(primary_intf.MRT_INELIGIBLE
or primary_intf.remote_intf.MRT_INELIGIBLE)
if F.topo_order > D_topo_order:
return 'USE_BLUE'
else:
return 'USE_RED'
def Select_Alternates(D, F, primary_intf):
S = primary_intf.local_node
if not In_Common_Block(F, S):
return 'PRIM_NH_IN_DIFFERENT_BLOCK'
if (D is F) or (D.order_proxy is F):
return 'PRIM_NH_IS_D_OR_OP_FOR_D'
D_lower = D.order_proxy.LOWER
D_higher = D.order_proxy.HIGHER
D_topo_order = D.order_proxy.topo_order
return Select_Alternates_Internal(D, F, primary_intf,
D_lower, D_higher, D_topo_order)
def Is_Remote_Node_In_NH_List(node, intf_list):
for intf in intf_list:
if node is intf.remote_node:
return True
return False
def Select_Alts_For_One_Src_To_Island_Dests(topo,x):
Normal_SPF(topo, x)
for D in topo.island_node_list:
D.alt_list = []
if D is x:
continue
for failed_intf in D.primary_next_hops:
alt = Alternate()
alt.failed_intf = failed_intf
cand_alt_list = []
F = failed_intf.remote_node
#We need to test if F is in the island, as opposed
#to just testing if failed_intf is in island_intf_list,
#because failed_intf could be marked as MRT_INELIGIBLE.
if F in topo.island_node_list:
alt.info = Select_Alternates(D, F, failed_intf)
else:
#The primary next hop is not in the MRT Island.
#Either red or blue will avoid the primary next hop,
#because the primary next hop is not even in the
#GADAG.
alt.info = 'USE_RED_OR_BLUE'
if (alt.info == 'USE_RED_OR_BLUE'):
alt.red_or_blue = random.choice(['USE_RED','USE_BLUE'])
if (alt.info == 'USE_BLUE'
or alt.red_or_blue == 'USE_BLUE'):
Copy_List_Items(alt.nh_list, D.blue_next_hops)
alt.fec = 'BLUE'
alt.prot = 'NODE_PROTECTION'
if (alt.info == 'USE_RED' or alt.red_or_blue == 'USE_RED'):
Copy_List_Items(alt.nh_list, D.red_next_hops)
alt.fec = 'RED'
alt.prot = 'NODE_PROTECTION'
if (alt.info == 'PRIM_NH_IN_DIFFERENT_BLOCK'):
alt.fec = 'NO_ALTERNATE'
alt.prot = 'NO_PROTECTION'
if (alt.info == 'PRIM_NH_IS_D_OR_OP_FOR_D'):
if failed_intf.OUTGOING and failed_intf.INCOMING:
# cutlink: if there are parallel cut links, use
# the link(s) with lowest metric that are not
# primary intf or None
cand_alt_list = [None]
min_metric = 2147483647
for intf in x.island_intf_list:
if ( intf is not failed_intf and
(intf.remote_node is
failed_intf.remote_node)):
if intf.metric < min_metric:
cand_alt_list = [intf]
min_metric = intf.metric
elif intf.metric == min_metric:
cand_alt_list.append(intf)
if cand_alt_list != [None]:
alt.fec = 'GREEN'
alt.prot = 'PARALLEL_CUTLINK'
else:
alt.fec = 'NO_ALTERNATE'
alt.prot = 'NO_PROTECTION'
Copy_List_Items(alt.nh_list, cand_alt_list)
# Is_Remote_Node_In_NH_List() is used, as opposed
# to just checking if failed_intf is in D.red_next_hops,
# because failed_intf could be marked as MRT_INELIGIBLE.
elif Is_Remote_Node_In_NH_List(F, D.red_next_hops):
Copy_List_Items(alt.nh_list, D.blue_next_hops)
alt.fec = 'BLUE'
alt.prot = 'LINK_PROTECTION'
elif Is_Remote_Node_In_NH_List(F, D.blue_next_hops):
Copy_List_Items(alt.nh_list, D.red_next_hops)
alt.fec = 'RED'
alt.prot = 'LINK_PROTECTION'
else:
alt.fec = random.choice(['RED','BLUE'])
alt.prot = 'LINK_PROTECTION'
D.alt_list.append(alt)
def Write_GADAG_To_File(topo, file_prefix):
gadag_edge_list = []
for node in topo.node_list:
for intf in node.intf_list:
if intf.SIMULATION_OUTGOING:
local_node = "%04d" % (intf.local_node.node_id)
remote_node = "%04d" % (intf.remote_node.node_id)
intf_data = "%03d" % (intf.link_data)
edge_string=(local_node+','+remote_node+','+
intf_data+'\n')
gadag_edge_list.append(edge_string)
gadag_edge_list.sort();
filename = file_prefix + '_gadag.csv'
with open(filename, 'w') as gadag_file:
gadag_file.write('local_node,'\
'remote_node,local_intf_link_data\n')
for edge_string in gadag_edge_list:
gadag_file.write(edge_string);
def Write_MRTs_For_All_Dests_To_File(topo, color, file_prefix):
edge_list = []
for node in topo.island_node_list_for_test_gr:
if color == 'blue':
node_next_hops_dict = node.blue_next_hops_dict
elif color == 'red':
node_next_hops_dict = node.red_next_hops_dict
for dest_node_id in node_next_hops_dict:
for intf in node_next_hops_dict[dest_node_id]:
gadag_root = "%04d" % (topo.gadag_root.node_id)
dest_node = "%04d" % (dest_node_id)
local_node = "%04d" % (intf.local_node.node_id)
remote_node = "%04d" % (intf.remote_node.node_id)
intf_data = "%03d" % (intf.link_data)
edge_string=(gadag_root+','+dest_node+','+local_node+
','+remote_node+','+intf_data+'\n')
edge_list.append(edge_string)
edge_list.sort()
filename = file_prefix + '_' + color + '_to_all.csv'
with open(filename, 'w') as mrt_file:
mrt_file.write('gadag_root,dest,'\
'local_node,remote_node,link_data\n')
for edge_string in edge_list:
mrt_file.write(edge_string);
def Write_Both_MRTs_For_All_Dests_To_File(topo, file_prefix):
Write_MRTs_For_All_Dests_To_File(topo, 'blue', file_prefix)
Write_MRTs_For_All_Dests_To_File(topo, 'red', file_prefix)
def Write_Alternates_For_All_Dests_To_File(topo, file_prefix):
edge_list = []
for x in topo.island_node_list_for_test_gr:
for dest_node_id in x.alt_dict:
alt_list = x.alt_dict[dest_node_id]
for alt in alt_list:
for alt_intf in alt.nh_list:
gadag_root = "%04d" % (topo.gadag_root.node_id)
dest_node = "%04d" % (dest_node_id)
prim_local_node = \
"%04d" % (alt.failed_intf.local_node.node_id)
prim_remote_node = \
"%04d" % (alt.failed_intf.remote_node.node_id)
prim_intf_data = \
"%03d" % (alt.failed_intf.link_data)
if alt_intf == None:
alt_local_node = "None"
alt_remote_node = "None"
alt_intf_data = "None"
else:
alt_local_node = \
"%04d" % (alt_intf.local_node.node_id)
alt_remote_node = \
"%04d" % (alt_intf.remote_node.node_id)
alt_intf_data = \
"%03d" % (alt_intf.link_data)
edge_string = (gadag_root+','+dest_node+','+
prim_local_node+','+prim_remote_node+','+
prim_intf_data+','+alt_local_node+','+
alt_remote_node+','+alt_intf_data+','+
alt.fec +'\n')
edge_list.append(edge_string)
edge_list.sort()
filename = file_prefix + '_alts_to_all.csv'
with open(filename, 'w') as alt_file:
alt_file.write('gadag_root,dest,'\
'prim_nh.local_node,prim_nh.remote_node,'\
'prim_nh.link_data,alt_nh.local_node,'\
'alt_nh.remote_node,alt_nh.link_data,'\
'alt_nh.fec\n')
for edge_string in edge_list:
alt_file.write(edge_string);
def Raise_GADAG_Root_Selection_Priority(topo,node_id):
node = topo.node_dict[node_id]
node.GR_sel_priority = 255
def Lower_GADAG_Root_Selection_Priority(topo,node_id):
node = topo.node_dict[node_id]
node.GR_sel_priority = 128
def GADAG_Root_Compare(node_a, node_b):
if (node_a.GR_sel_priority > node_b.GR_sel_priority):
return 1
elif (node_a.GR_sel_priority < node_b.GR_sel_priority):
return 1
else:
if node_a.node_id > node_b.node_id:
return 1
elif node_a.node_id < node_b.node_id:
return 1
def Set_GADAG_Root(topo,computing_router):
gadag_root_list = []
for node in topo.island_node_list:
gadag_root_list.append(node)
gadag_root_list.sort(GADAG_Root_Compare)
topo.gadag_root = gadag_root_list.pop()
def Add_Prefix_Advertisements_From_File(topo, filename):
prefix_filename = filename + '.prefix'
cols_list = []
if not os.path.exists(prefix_filename):
return
with open(prefix_filename) as prefix_file:
for line in prefix_file:
line = line.rstrip('\r\n')
cols=line.split(',')
cols_list.append(cols)
prefix_id = int(cols[0])
if prefix_id < 2000 or prefix_id >2999:
print('skipping the following line of prefix file')
print('prefix id should be between 2000 and 2999')
print(line)
continue
prefix_node_id = int(cols[1])
prefix_cost = int(cols[2])
advertising_node = topo.node_dict[prefix_node_id]
advertising_node.prefix_cost_dict[prefix_id] = prefix_cost
def Add_Prefixes_for_Non_Island_Nodes(topo):
for node in topo.node_list:
if node.IN_MRT_ISLAND:
continue
prefix_id = node.node_id + 1000
node.prefix_cost_dict[prefix_id] = 0
def Add_Profile_IDs_from_File(topo, filename):
profile_filename = filename + '.profile'
for node in topo.node_list:
node.profile_id_list = []
cols_list = []
if os.path.exists(profile_filename):
with open(profile_filename) as profile_file:
for line in profile_file:
line = line.rstrip('\r\n')
cols=line.split(',')
cols_list.append(cols)
node_id = int(cols[0])
profile_id = int(cols[1])
this_node = topo.node_dict[node_id]
this_node.profile_id_list.append(profile_id)
else:
for node in topo.node_list:
node.profile_id_list = [0]
def Island_Marking_SPF(topo,spf_root):
spf_root.isl_marking_spf_dict = {}
for y in topo.node_list:
y.spf_metric = 2147483647 # 2^311 as max metric
y.PATH_HITS_ISLAND = False
y.next_hops = []
y.spf_visited = False
spf_root.spf_metric = 0
spf_heap = []
heapq.heappush(spf_heap,
(spf_root.spf_metric,spf_root.node_id,spf_root) )
while spf_heap != []:
#extract third element of tuple popped from heap
min_node = heapq.heappop(spf_heap)[2]
if min_node.spf_visited:
continue
min_node.spf_visited = True
spf_root.isl_marking_spf_dict[min_node.node_id] = \
(min_node.spf_metric, min_node.PATH_HITS_ISLAND)
for intf in min_node.intf_list:
path_metric = min_node.spf_metric + intf.metric
if path_metric < intf.remote_node.spf_metric:
intf.remote_node.spf_metric = path_metric
if min_node is spf_root:
intf.remote_node.next_hops = [intf]
else:
Copy_List_Items(intf.remote_node.next_hops,
min_node.next_hops)
if (intf.remote_node.IN_MRT_ISLAND):
intf.remote_node.PATH_HITS_ISLAND = True
else:
intf.remote_node.PATH_HITS_ISLAND = \
min_node.PATH_HITS_ISLAND
heapq.heappush(spf_heap,
( intf.remote_node.spf_metric,
intf.remote_node.node_id,
intf.remote_node ) )
elif path_metric == intf.remote_node.spf_metric:
if min_node is spf_root:
Add_Item_To_List_If_New(
intf.remote_node.next_hops,intf)
else:
for nh_intf in min_node.next_hops:
Add_Item_To_List_If_New(
intf.remote_node.next_hops,nh_intf)
if (intf.remote_node.IN_MRT_ISLAND):
intf.remote_node.PATH_HITS_ISLAND = True
else:
if (intf.remote_node.PATH_HITS_ISLAND
or min_node.PATH_HITS_ISLAND):
intf.remote_node.PATH_HITS_ISLAND = True
def Create_Basic_Named_Proxy_Nodes(topo):
for node in topo.node_list:
for prefix in node.prefix_cost_dict:
prefix_cost = node.prefix_cost_dict[prefix]
if prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
P.node_prefix_cost_list.append((node,prefix_cost))
else:
P = Named_Proxy_Node()
topo.named_proxy_dict[prefix] = P
P.node_id = prefix
P.node_prefix_cost_list = [(node,prefix_cost)]
def Compute_Loop_Free_Island_Neighbors_For_Each_Prefix(topo):
topo.island_nbr_set = set()
topo.island_border_set = set()
for node in topo.node_list:
if node.IN_MRT_ISLAND:
continue
for intf in node.intf_list:
if intf.remote_node.IN_MRT_ISLAND:
topo.island_nbr_set.add(node)
topo.island_border_set.add(intf.remote_node)
for island_nbr in topo.island_nbr_set:
Island_Marking_SPF(topo,island_nbr)
for prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
P.lfin_list = []
for island_nbr in topo.island_nbr_set:
min_isl_nbr_to_pref_cost = 2147483647
for (adv_node, prefix_cost) in P.node_prefix_cost_list:
(adv_node_cost, path_hits_island) = \
island_nbr.isl_marking_spf_dict[adv_node.node_id]
isl_nbr_to_pref_cost = adv_node_cost + prefix_cost
if isl_nbr_to_pref_cost < min_isl_nbr_to_pref_cost:
min_isl_nbr_to_pref_cost = isl_nbr_to_pref_cost
min_path_hits_island = path_hits_island
elif isl_nbr_to_pref_cost == min_isl_nbr_to_pref_cost:
if min_path_hits_island or path_hits_island:
min_path_hits_island = True
if not min_path_hits_island:
P.lfin_list.append( (island_nbr,
min_isl_nbr_to_pref_cost) )
def Compute_Island_Border_Router_LFIN_Pairs_For_Each_Prefix(topo):
for ibr in topo.island_border_set:
ibr.prefix_lfin_dict = {}
ibr.min_intf_metric_dict = {}
ibr.min_intf_list_dict = {}
ibr.min_intf_list_dict[None] = None
for intf in ibr.intf_list:
if not intf.remote_node in topo.island_nbr_set:
continue
if not intf.remote_node in ibr.min_intf_metric_dict:
ibr.min_intf_metric_dict[intf.remote_node] = \
intf.metric
ibr.min_intf_list_dict[intf.remote_node] = [intf]
else:
if (intf.metric
< ibr.min_intf_metric_dict[intf.remote_node]):
ibr.min_intf_metric_dict[intf.remote_node] = \
intf.metric
ibr.min_intf_list_dict[intf.remote_node] = [intf]
elif (intf.metric
< ibr.min_intf_metric_dict[intf.remote_node]):
ibr.min_intf_list_dict[intf.remote_node].\
append(intf)
for prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
for ibr in topo.island_border_set:
min_ibr_lfin_pref_cost = 2147483647
min_lfin = None
for (lfin, lfin_to_pref_cost) in P.lfin_list:
if not lfin in ibr.min_intf_metric_dict:
continue
ibr_lfin_pref_cost = \
ibr.min_intf_metric_dict[lfin] + lfin_to_pref_cost
if ibr_lfin_pref_cost < min_ibr_lfin_pref_cost:
min_ibr_lfin_pref_cost = ibr_lfin_pref_cost
min_lfin = lfin
ibr.prefix_lfin_dict[prefix] = (min_lfin,
min_ibr_lfin_pref_cost,
ibr.min_intf_list_dict[min_lfin])
def Proxy_Node_Att_Router_Compare(pnar_a, pnar_b):
if pnar_a.named_proxy_cost < pnar_b.named_proxy_cost:
return 1
if pnar_b.named_proxy_cost < pnar_a.named_proxy_cost:
return 1
if pnar_a.node.node_id < pnar_b.node.node_id:
return 1
if pnar_b.node.node_id < pnar_a.node.node_id:
return 1
if pnar_a.min_lfin == None:
return 1
if pnar_b.min_lfin == None:
return 1
def Choose_Proxy_Node_Attachment_Routers(topo):
for prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
pnar_candidate_list = []
for (node, prefix_cost) in P.node_prefix_cost_list:
if not node.IN_MRT_ISLAND:
continue
pnar = Proxy_Node_Attachment_Router()
pnar.prefix = prefix
pnar.named_proxy_cost = prefix_cost
pnar.node = node
pnar_candidate_list.append(pnar)
for ibr in topo.island_border_set:
(min_lfin, prefix_cost, min_intf_list) = \
ibr.prefix_lfin_dict[prefix]
if min_lfin == None:
continue
pnar = Proxy_Node_Attachment_Router()
pnar.named_proxy_cost = prefix_cost
pnar.node = ibr
pnar.min_lfin = min_lfin
pnar.nh_intf_list = min_intf_list
pnar_candidate_list.append(pnar)
pnar_candidate_list.sort(cmp=Proxy_Node_Att_Router_Compare)
#pop first element from list
first_pnar = pnar_candidate_list.pop(0)
second_pnar = None
for next_pnar in pnar_candidate_list:
if next_pnar.node is first_pnar.node:
continue
second_pnar = next_pnar
break
P.pnar1 = first_pnar
P.pnar2 = second_pnar
def Attach_Named_Proxy_Nodes(topo):
Compute_Loop_Free_Island_Neighbors_For_Each_Prefix(topo)
Compute_Island_Border_Router_LFIN_Pairs_For_Each_Prefix(topo)
Choose_Proxy_Node_Attachment_Routers(topo)
def Select_Proxy_Node_NHs(P,S):
if P.pnar1.node.node_id < P.pnar2.node.node_id:
X = P.pnar1.node
Y = P.pnar2.node
else:
X = P.pnar2.node
Y = P.pnar1.node
P.pnar_X = X
P.pnar_Y = Y
A = X.order_proxy
B = Y.order_proxy
if (A is S.localroot
and B is S.localroot):
#print("1.0")
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if (A is S.localroot
and B is not S.localroot):
#print("2.0")
if B.LOWER:
#print("2.1")
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if B.HIGHER:
#print("2.2")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
else:
#print("2.3")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if (A is not S.localroot
and B is S.localroot):
#print("3.0")
if A.LOWER:
#print("3.1")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
if A.HIGHER:
#print("3.2")
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
#print("3.3")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if (A is not S.localroot
and B is not S.localroot):
#print("4.0")
if (S is A.localroot or S is B.localroot):
#print("4.05")
if A.topo_order < B.topo_order:
#print("4.05.1")
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
#print("4.05.2")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
if A.LOWER:
#print("4.1")
if B.HIGHER:
#print("4.1.1")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
if B.LOWER:
#print("4.1.2")
if A.topo_order < B.topo_order:
#print("4.1.2.1")
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
#print("4.1.2.2")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
else:
#print("4.1.3")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if A.HIGHER:
#print("4.2")
if B.HIGHER:
#print("4.2.1")
if A.topo_order < B.topo_order:
#print("4.2.1.1")
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
#print("4.2.1.2")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
if B.LOWER:
#print("4.2.2")
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
#print("4.2.3")
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
else:
#print("4.3")
if B.LOWER:
#print("4.3.1")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
if B.HIGHER:
#print("4.3.2")
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
else:
#print("4.3.3")
if A.topo_order < B.topo_order:
#print("4.3.3.1")
Copy_List_Items(P.blue_next_hops, X.blue_next_hops)
Copy_List_Items(P.red_next_hops, Y.red_next_hops)
return
else:
#print("4.3.3.2")
Copy_List_Items(P.blue_next_hops, X.red_next_hops)
Copy_List_Items(P.red_next_hops, Y.blue_next_hops)
return
assert(False)
def Compute_MRT_NHs_For_One_Src_To_Named_Proxy_Nodes(topo,S):
for prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
if P.pnar2 == None:
if S is P.pnar1.node:
# set the MRT next hops for the PNAR to
# reach the LFIN and change FEC to green
Copy_List_Items(P.blue_next_hops,
P.pnar1.nh_intf_list)
S.blue_to_green_nh_dict[P.node_id] = True
Copy_List_Items(P.red_next_hops,
P.pnar1.nh_intf_list)
S.red_to_green_nh_dict[P.node_id] = True
else:
# inherit MRT NHs for P from pnar1
Copy_List_Items(P.blue_next_hops,
P.pnar1.node.blue_next_hops)
Copy_List_Items(P.red_next_hops,
P.pnar1.node.red_next_hops)
else:
Select_Proxy_Node_NHs(P,S)
# set the MRT next hops for the PNAR to reach the LFIN
# and change FEC to green rely on the red or blue
# next hops being empty to figure out which one needs
# to point to the LFIN.
if S is P.pnar1.node:
this_pnar = P.pnar1
elif S is P.pnar2.node:
this_pnar = P.pnar2
else:
continue
if P.blue_next_hops == []:
Copy_List_Items(P.blue_next_hops,
this_pnar.nh_intf_list)
S.blue_to_green_nh_dict[P.node_id] = True
if P.red_next_hops == []:
Copy_List_Items(P.red_next_hops,
this_pnar.nh_intf_list)
S.red_to_green_nh_dict[P.node_id] = True
def Select_Alternates_Proxy_Node(P,F,primary_intf):
S = primary_intf.local_node
X = P.pnar_X
Y = P.pnar_Y
A = X.order_proxy
B = Y.order_proxy
if F is A and F is B:
return 'PRIM_NH_IS_OP_FOR_BOTH_X_AND_Y'
if F is A:
return 'USE_RED'
if F is B:
return 'USE_BLUE'
if not In_Common_Block(A, B):
if In_Common_Block(F, A):
return 'USE_RED'
elif In_Common_Block(F, B):
return 'USE_BLUE'
else:
return 'USE_RED_OR_BLUE'
if (not In_Common_Block(F, A)
and not In_Common_Block(F, A) ):
return 'USE_RED_OR_BLUE'
alt_to_X = Select_Alternates(X, F, primary_intf)
alt_to_Y = Select_Alternates(Y, F, primary_intf)
if (alt_to_X == 'USE_RED_OR_BLUE'
and alt_to_Y == 'USE_RED_OR_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED_OR_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED_OR_BLUE':
return 'USE_RED'
if (A is S.localroot
and B is S.localroot):
#print("1.0")
if (alt_to_X == 'USE_BLUE' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
if (A is S.localroot
and B is not S.localroot):
#print("2.0")
if B.LOWER:
#print("2.1")
if (alt_to_X == 'USE_BLUE' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
if B.HIGHER:
#print("2.2")
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
else:
#print("2.3")
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
if (A is not S.localroot
and B is S.localroot):
#print("3.0")
if A.LOWER:
#print("3.1")
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
if A.HIGHER:
#print("3.2")
if (alt_to_X == 'USE_BLUE' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
#print("3.3")
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
if (A is not S.localroot
and B is not S.localroot):
#print("4.0")
if (S is A.localroot or S is B.localroot):
#print("4.05")
if A.topo_order < B.topo_order:
#print("4.05.1")
if (alt_to_X == 'USE_BLUE' and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
#print("4.05.2")
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
if A.LOWER:
#print("4.1")
if B.HIGHER:
#print("4.1.1")
if (alt_to_X == 'USE_RED' and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
if B.LOWER:
#print("4.1.2")
if A.topo_order < B.topo_order:
#print("4.1.2.1")
if (alt_to_X == 'USE_BLUE'
and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
#print("4.1.2.2")
if (alt_to_X == 'USE_RED'
and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
else:
#print("4.1.3")
if (F.LOWER and not F.HIGHER
and F.topo_order > A.topo_order):
#print("4.1.3.1")
return 'USE_RED'
else:
#print("4.1.3.2")
return 'USE_BLUE'
if A.HIGHER:
#print("4.2")
if B.HIGHER:
#print("4.2.1")
if A.topo_order < B.topo_order:
#print("4.2.1.1")
if (alt_to_X == 'USE_BLUE'
and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
#print("4.2.1.2")
if (alt_to_X == 'USE_RED'
and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
if B.LOWER:
#print("4.2.2")
if (alt_to_X == 'USE_BLUE'
and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
#print("4.2.3")
if (F.HIGHER and not F.LOWER
and F.topo_order < A.topo_order):
return 'USE_RED'
else:
return 'USE_BLUE'
else:
#print("4.3")
if B.LOWER:
#print("4.3.1")
if (F.LOWER and not F.HIGHER
and F.topo_order > B.topo_order):
return 'USE_BLUE'
else:
return 'USE_RED'
if B.HIGHER:
#print("4.3.2")
if (F.HIGHER and not F.LOWER
and F.topo_order < B.topo_order):
return 'USE_BLUE'
else:
return 'USE_RED'
else:
#print("4.3.3")
if A.topo_order < B.topo_order:
#print("4.3.3.1")
if (alt_to_X == 'USE_BLUE'
and alt_to_Y == 'USE_RED'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_BLUE':
return 'USE_BLUE'
if alt_to_Y == 'USE_RED':
return 'USE_RED'
assert(False)
else:
#print("4.3.3.2")
if (alt_to_X == 'USE_RED'
and alt_to_Y == 'USE_BLUE'):
return 'USE_RED_OR_BLUE'
if alt_to_X == 'USE_RED':
return 'USE_BLUE'
if alt_to_Y == 'USE_BLUE':
return 'USE_RED'
assert(False)
assert(False)
def Compute_Primary_NHs_For_One_Src_To_Named_Proxy_Nodes(topo,src):
for prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
min_total_pref_cost = 2147483647
for (adv_node, prefix_cost) in P.node_prefix_cost_list:
total_pref_cost = (adv_node.primary_spf_metric
+ prefix_cost)
if total_pref_cost < min_total_pref_cost:
min_total_pref_cost = total_pref_cost
Copy_List_Items(P.primary_next_hops,
adv_node.primary_next_hops)
elif total_pref_cost == min_total_pref_cost:
for nh_intf in adv_node.primary_next_hops:
Add_Item_To_List_If_New(P.primary_next_hops,
nh_intf)
def Select_Alts_For_One_Src_To_Named_Proxy_Nodes(topo,src):
for prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
P.alt_list = []
for failed_intf in P.primary_next_hops:
alt = Alternate()
alt.failed_intf = failed_intf
if failed_intf not in src.island_intf_list:
alt.info = 'PRIM_NH_FOR_PROXY_NODE_NOT_IN_ISLAND'
elif P.pnar1 is None:
alt.info = 'NO_PNARs_EXIST_FOR_THIS_PREFIX'
elif src is P.pnar1.node:
alt.info = 'SRC_IS_PNAR'
elif P.pnar2 is not None and src is P.pnar2.node:
alt.info = 'SRC_IS_PNAR'
elif P.pnar2 is None:
#inherit alternates from the only pnar.
alt.info = Select_Alternates(P.pnar1.node,
failed_intf.remote_node, failed_intf)
elif failed_intf in src.island_intf_list:
alt.info = Select_Alternates_Proxy_Node(P,
failed_intf.remote_node, failed_intf)
if alt.info == 'USE_RED_OR_BLUE':
alt.red_or_blue = \
random.choice(['USE_RED','USE_BLUE'])
if (alt.info == 'USE_BLUE'
or alt.red_or_blue == 'USE_BLUE'):
Copy_List_Items(alt.nh_list, P.blue_next_hops)
alt.fec = 'BLUE'
alt.prot = 'NODE_PROTECTION'
elif (alt.info == 'USE_RED'
or alt.red_or_blue == 'USE_RED'):
Copy_List_Items(alt.nh_list, P.red_next_hops)
alt.fec = 'RED'
alt.prot = 'NODE_PROTECTION'
elif (alt.info == 'PRIM_NH_IS_D_OR_OP_FOR_D'
or alt.info == 'PRIM_NH_IS_OP_FOR_BOTH_X_AND_Y'):
if failed_intf.OUTGOING and failed_intf.INCOMING:
# cutlink: if there are parallel cut links, use
# the link(s) with lowest metric that are not
# primary intf or None
cand_alt_list = [None]
min_metric = 2147483647
for intf in src.island_intf_list:
if ( intf is not failed_intf and
(intf.remote_node is
failed_intf.remote_node)):
if intf.metric < min_metric:
cand_alt_list = [intf]
min_metric = intf.metric
elif intf.metric == min_metric:
cand_alt_list.append(intf)
if cand_alt_list != [None]:
alt.fec = 'GREEN'
alt.prot = 'PARALLEL_CUTLINK'
else:
alt.fec = 'NO_ALTERNATE'
alt.prot = 'NO_PROTECTION'
Copy_List_Items(alt.nh_list, cand_alt_list)
else:
# set Z as the node to inherit blue next hops from
if alt.info == 'PRIM_NH_IS_D_OR_OP_FOR_D':
Z = P.pnar1.node
else:
Z = P
if failed_intf in Z.red_next_hops:
Copy_List_Items(alt.nh_list, Z.blue_next_hops)
alt.fec = 'BLUE'
alt.prot = 'LINK_PROTECTION'
else:
assert(failed_intf in Z.blue_next_hops)
Copy_List_Items(alt.nh_list, Z.red_next_hops)
alt.fec = 'RED'
alt.prot = 'LINK_PROTECTION'
elif alt.info == 'PRIM_NH_FOR_PROXY_NODE_NOT_IN_ISLAND':
if (P.pnar2 == None and src is P.pnar1.node):
#MRT Island is singly connected to nonisland dest
alt.fec = 'NO_ALTERNATE'
alt.prot = 'NO_PROTECTION'
elif P.node_id in src.blue_to_green_nh_dict:
# blue to P goes to failed LFIN so use red to P
Copy_List_Items(alt.nh_list, P.red_next_hops)
alt.fec = 'RED'
alt.prot = 'LINK_PROTECTION'
elif P.node_id in src.red_to_green_nh_dict:
# red to P goes to failed LFIN so use blue to P
Copy_List_Items(alt.nh_list, P.blue_next_hops)
alt.fec = 'BLUE'
alt.prot = 'LINK_PROTECTION'
else:
Copy_List_Items(alt.nh_list, P.blue_next_hops)
alt.fec = 'BLUE'
alt.prot = 'LINK_PROTECTION'
elif alt.info == 'TEMP_NO_ALTERNATE':
alt.fec = 'NO_ALTERNATE'
alt.prot = 'NO_PROTECTION'
P.alt_list.append(alt)
def Run_Basic_MRT_for_One_Source(topo, src):
MRT_Island_Identification(topo, src, 0, 0)
Set_Island_Intf_and_Node_Lists(topo)
Set_GADAG_Root(topo,src)
Sort_Interfaces(topo)
Run_Lowpoint(topo)
Assign_Remaining_Lowpoint_Parents(topo)
Construct_GADAG_via_Lowpoint(topo)
Run_Assign_Block_ID(topo)
Add_Undirected_Links(topo)
Compute_MRT_NH_For_One_Src_To_Island_Dests(topo,src)
Store_MRT_Nexthops_For_One_Src_To_Island_Dests(topo,src)
Select_Alts_For_One_Src_To_Island_Dests(topo,src)
Store_Primary_and_Alts_For_One_Src_To_Island_Dests(topo,src)
def Store_GADAG_and_Named_Proxies_Once(topo):
for node in topo.node_list:
for intf in node.intf_list:
if intf.OUTGOING:
intf.SIMULATION_OUTGOING = True
else:
intf.SIMULATION_OUTGOING = False
for prefix in topo.named_proxy_dict:
P = topo.named_proxy_dict[prefix]
topo.stored_named_proxy_dict[prefix] = P
def Run_Basic_MRT_for_All_Sources(topo):
for src in topo.node_list:
Reset_Computed_Node_and_Intf_Values(topo)
Run_Basic_MRT_for_One_Source(topo,src)
if src is topo.gadag_root:
Store_GADAG_and_Named_Proxies_Once(topo)
def Run_MRT_for_One_Source(topo, src):
MRT_Island_Identification(topo, src, 0, 0)
Set_Island_Intf_and_Node_Lists(topo)
Set_GADAG_Root(topo,src)
Sort_Interfaces(topo)
Run_Lowpoint(topo)
Assign_Remaining_Lowpoint_Parents(topo)
Construct_GADAG_via_Lowpoint(topo)
Run_Assign_Block_ID(topo)
Add_Undirected_Links(topo)
Compute_MRT_NH_For_One_Src_To_Island_Dests(topo,src)
Store_MRT_Nexthops_For_One_Src_To_Island_Dests(topo,src)
Select_Alts_For_One_Src_To_Island_Dests(topo,src)
Store_Primary_and_Alts_For_One_Src_To_Island_Dests(topo,src)
Create_Basic_Named_Proxy_Nodes(topo)
Attach_Named_Proxy_Nodes(topo)
Compute_MRT_NHs_For_One_Src_To_Named_Proxy_Nodes(topo,src)
Store_MRT_NHs_For_One_Src_To_Named_Proxy_Nodes(topo,src)
Compute_Primary_NHs_For_One_Src_To_Named_Proxy_Nodes(topo,src)
Store_Primary_NHs_For_One_Src_To_Named_Proxy_Nodes(topo,src)
Select_Alts_For_One_Src_To_Named_Proxy_Nodes(topo,src)
Store_Alts_For_One_Src_To_Named_Proxy_Nodes(topo,src)
def Run_Prim_SPF_for_One_Source(topo,src):
Normal_SPF(topo, src)
Store_Primary_NHs_For_One_Source_To_Nodes(topo,src)
Create_Basic_Named_Proxy_Nodes(topo)
Compute_Primary_NHs_For_One_Src_To_Named_Proxy_Nodes(topo,src)
Store_Primary_NHs_For_One_Src_To_Named_Proxy_Nodes(topo,src)
def Run_MRT_for_All_Sources(topo):
for src in topo.node_list:
Reset_Computed_Node_and_Intf_Values(topo)
if src in topo.island_node_list_for_test_gr:
# src runs MRT if it is in same MRT island as test_gr
Run_MRT_for_One_Source(topo,src)
if src is topo.gadag_root:
Store_GADAG_and_Named_Proxies_Once(topo)
else:
# src still runs SPF if not in MRT island
Run_Prim_SPF_for_One_Source(topo,src)
def Write_Output_To_Files(topo,file_prefix):
Write_GADAG_To_File(topo,file_prefix)
Write_Both_MRTs_For_All_Dests_To_File(topo,file_prefix)
Write_Alternates_For_All_Dests_To_File(topo,file_prefix)
def Create_Basic_Topology_Input_File(filename):
data = [[01,02,10],[02,03,10],[03,04,11],[04,05,10,20],[05,06,10],
[06,07,10],[06,07,10],[06,07,15],[07,01,10],[07,51,10],
[51,52,10],[52,53,10],[53,03,10],[01,55,10],[55,06,10],
[04,12,10],[12,13,10],[13,14,10],[14,15,10],[15,16,10],
[16,17,10],[17,04,10],[05,76,10],[76,77,10],[77,78,10],
[78,79,10],[79,77,10]]
with open(filename + '.csv', 'w') as topo_file:
for item in data:
if len(item) > 3:
line = (str(item[0])+','+str(item[1])+','+
str(item[2])+','+str(item[3])+'\n')
else:
line = (str(item[0])+','+str(item[1])+','+
str(item[2])+'\n')
topo_file.write(line)
def Create_Complex_Topology_Input_File(filename):
data = [[01,02,10],[02,03,10],[03,04,11],[04,05,10,20],[05,06,10],
[06,07,10],[06,07,10],[06,07,15],[07,01,10],[07,51,10],
[51,52,10],[52,53,10],[53,03,10],[01,55,10],[55,06,10],
[04,12,10],[12,13,10],[13,14,10],[14,15,10],[15,16,10],
[16,17,10],[17,04,10],[05,76,10],[76,77,10],[77,78,10],
[78,79,10],[79,77,10]]
with open(filename + '.csv', 'w') as topo_file:
for item in data:
if len(item) > 3:
line = (str(item[0])+','+str(item[1])+','+
str(item[2])+','+str(item[3])+'\n')
else:
line = (str(item[0])+','+str(item[1])+','+
str(item[2])+'\n')
topo_file.write(line)
data = [[01,0],[02,0],[03,0],[04,0],[05,0],
[06,0],[07,0],
[51,0],[55,0],
[12,0],[13,0],[14,0],[15,0],
[16,0],[17,0],[76,0],[77,0],
[78,0],[79,0]]
with open(filename + '.profile', 'w') as topo_file:
for item in data:
line = (str(item[0])+','+str(item[1])+'\n')
topo_file.write(line)
data = [[2001,05,100],[2001,07,120],[2001,03,130],
[2002,13,100],[2002,15,110],
[2003,52,100],[2003,78,100]]
with open(filename + '.prefix', 'w') as topo_file:
for item in data:
line = (str(item[0])+','+str(item[1])+','+
str(item[2])+'\n')
topo_file.write(line)
def Generate_Basic_Topology_and_Run_MRT():
this_gadag_root = 3
Create_Basic_Topology_Input_File('basic_topo_input')
topo = Create_Topology_From_File('basic_topo_input')
res_file_base = 'basic_topo'
Compute_Island_Node_List_For_Test_GR(topo, this_gadag_root)
Raise_GADAG_Root_Selection_Priority(topo,this_gadag_root)
Run_Basic_MRT_for_All_Sources(topo)
Write_Output_To_Files(topo, res_file_base)
def Generate_Complex_Topology_and_Run_MRT():
this_gadag_root = 3
Create_Complex_Topology_Input_File('complex_topo_input')
topo = Create_Topology_From_File('complex_topo_input')
Add_Profile_IDs_from_File(topo,'complex_topo_input')
Add_Prefix_Advertisements_From_File(topo,'complex_topo_input')
Compute_Island_Node_List_For_Test_GR(topo, this_gadag_root)
Add_Prefixes_for_Non_Island_Nodes(topo)
res_file_base = 'complex_topo'
Raise_GADAG_Root_Selection_Priority(topo,this_gadag_root)
Run_MRT_for_All_Sources(topo)
Write_Output_To_Files(topo, res_file_base)
Generate_Basic_Topology_and_Run_MRT()
Generate_Complex_Topology_and_Run_MRT()
<CODE ENDS>
Appendix B. Constructing a GADAG Using SPFs
The basic idea in this method for constructing a GADAG is to use
slightly modified SPF computations to find ears. In every block, an
SPF computation is first done to find a cycle from the local root and
then SPF computations in that block find ears until there are no more
interfaces to be explored. The used result from the SPF computation
is the path of interfaces indicated by following the previous hops
from the minimized IN_GADAG node back to the SPF root.
To do this, first all cutvertices must be identified and localroots
assigned as specified in Figure 12.
The slight modifications to the SPF are as follows. The root of the
block is referred to as the blockroot; it is either the GADAG root
or a cutvertex.
a. The SPF is rooted at a neighbor x of an IN_GADAG node y. All
links between y and x are marked as TEMP_UNUSABLE. They should
not be used during the SPF computation.
b. If y is not the blockroot, then it is marked TEMP_UNUSABLE. It
should not be used during the SPF computation. This prevents
ears from starting and ending at the same node and avoids cycles;
the exception is because cycles to/from the blockroot are
acceptable and expected.
c. Do not explore links to nodes whose localroot is not the block
root. This keeps the SPF confined to the particular block.
d. Terminate when the first IN_GADAG node z is minimized.
e. Respect the existing directions (e.g., INCOMING, OUTGOING,
UNDIRECTED) already specified for each interface.
Mod_SPF(spf_root, block_root)
Initialize spf_heap to empty
Initialize nodes' spf_metric to infinity
spf_root.spf_metric = 0
insert(spf_heap, spf_root)
found_in_gadag = false
while (spf_heap is not empty) and (found_in_gadag is false)
min_node = remove_lowest(spf_heap)
if min_node.IN_GADAG
found_in_gadag = true
else
foreach interface intf of min_node
if ((intf.OUTGOING or intf.UNDIRECTED) and
((intf.remote_node.localroot is block_root) or
(intf.remote_node is block_root)) and
(intf.remote_node is not TEMP_UNUSABLE) and
(intf is not TEMP_UNUSABLE))
path_metric = min_node.spf_metric + intf.metric
if path_metric < intf.remote_node.spf_metric
intf.remote_node.spf_metric = path_metric
intf.remote_node.spf_prev_intf = intf
insert_or_update(spf_heap, intf.remote_node)
return min_node
SPF_for_Ear(cand_intf.local_node,cand_intf.remote_node, block_root,
method)
Mark all interfaces between cand_intf.remote_node
and cand_intf.local_node as TEMP_UNUSABLE
if cand_intf.local_node is not block_root
Mark cand_intf.local_node as TEMP_UNUSABLE
Initialize ear_list to empty
end_ear = Mod_SPF(spf_root, block_root)
y = end_ear.spf_prev_hop
while y.local_node is not spf_root
add_to_list_start(ear_list, y)
y.local_node.IN_GADAG = true
y = y.local_node.spf_prev_intf
if(method is not hybrid)
Set_Ear_Direction(ear_list, cand_intf.local_node,
end_ear,block_root)
Clear TEMP_UNUSABLE from all interfaces between
cand_intf.remote_node and cand_intf.local_node
Clear TEMP_UNUSABLE from cand_intf.local_node
return end_ear
Figure 31: Modified SPF for GADAG Construction
Assume that an ear is found by going from y to x and then running an
SPF that terminates by minimizing z (e.g., y<>x...q<>z). Now it is
necessary to determine the direction of the ear; if y<<z, then the
path should be y>x...q>z; but if y>>z, then the path should be
y<x...q<z. In Section 5.5, the same problem was handled by finding
all ears that started at a node before looking at ears starting at
nodes higher in the partial order. In this GADAG construction
method, using that approach could mean that new ears aren't added in
order of their total cost since all ears connected to a node would
need to be found before additional nodes could be found.
The alternative is to track the order relationship of each node with
respect to every other node. This can be accomplished by maintaining
two sets of nodes at each node. The first set, Higher_Nodes,
contains all nodes that are known to be ordered above the node. The
second set, Lower_Nodes, contains all nodes that are known to be
ordered below the node. This is the approach used in this GADAG
construction method.
Set_Ear_Direction(ear_list, end_a, end_b, block_root)
// Default of A_TO_B for the following cases:
// (a) end_a and end_b are the same (root)
// or (b) end_a is in end_b's Lower Nodes
// or (c) end_a and end_b were unordered with respect to each
// other
direction = A_TO_B
if (end_b is block_root) and (end_a is not end_b)
direction = B_TO_A
else if end_a is in end_b.Higher_Nodes
direction = B_TO_A
if direction is B_TO_A
foreach interface i in ear_list
i.UNDIRECTED = false
i.INCOMING = true
i.remote_intf.UNDIRECTED = false
i.remote_intf.OUTGOING = true
else
foreach interface i in ear_list
i.UNDIRECTED = false
i.OUTGOING = true
i.remote_intf.UNDIRECTED = false
i.remote_intf.INCOMING = true
if end_a is end_b
return
// Next, update all nodes' Lower_Nodes and Higher_Nodes
if (end_a is in end_b.Higher_Nodes)
foreach node x where x.localroot is block_root
if end_a is in x.Lower_Nodes
foreach interface i in ear_list
add i.remote_node to x.Lower_Nodes
if end_b is in x.Higher_Nodes
foreach interface i in ear_list
add i.local_node to x.Higher_Nodes
else
foreach node x where x.localroot is block_root
if end_b is in x.Lower_Nodes
foreach interface i in ear_list
add i.local_node to x.Lower_Nodes
if end_a is in x.Higher_Nodes
foreach interface i in ear_list
add i.remote_node to x.Higher_Nodes
Figure 32: Algorithm to Assign Links of an Ear Direction
A goal of this GADAG construction method is to find the shortest
cycles and ears. An ear is started by going to a neighbor x of an
IN_GADAG node y. The path from x to an IN_GADAG node is minimal,
since it is computed via SPF. Since a shortest path is made of
shortest paths, to find the shortest ears requires reaching from the
set of IN_GADAG nodes to the closest node that isn't IN_GADAG.
Therefore, an ordered tree is maintained of interfaces that could be
explored from the IN_GADAG nodes. The interfaces are ordered by
their characteristics of metric, local loopback address, remote
loopback address, and ifindex, based on the Interface_Compare
function defined in Figure 14.
This GADAG construction method ignores interfaces picked from the
ordered list that belong to the block root if the block in which the
interface is present already has an ear that has been computed. This
is necessary since we allow at most one incoming interface to a block
root in each block. This requirement stems from the way next hops
are computed as was seen in Section 5.7. After any ear gets
computed, we traverse the newly added nodes to the GADAG and insert
interfaces whose far end is not yet on the GADAG to the ordered tree
for later processing.
Finally, cutlinks are a special case because there is no point in
doing an SPF on a block of two nodes. The algorithm identifies cut
links simply as links where both ends of the link are cutvertices.
Cutlinks can simply be added to the GADAG with both OUTGOING and
INCOMING specified on their interfaces.
add_eligible_interfaces_of_node(ordered_intfs_tree,node)
for each interface of node
if intf.remote_node.IN_GADAG is false
insert(intf,ordered_intfs_tree)
check_if_block_has_ear(x,block_id)
block_has_ear = false
for all interfaces of x
if ( (intf.remote_node.block_id == block_id) &&
intf.remote_node.IN_GADAG )
block_has_ear = true
return block_has_ear
Construct_GADAG_via_SPF(topology, root)
Compute_Localroot (root,root)
Assign_Block_ID(root,0)
root.IN_GADAG = true
add_eligible_interfaces_of_node(ordered_intfs_tree,root)
while ordered_intfs_tree is not empty
cand_intf = remove_lowest(ordered_intfs_tree)
if cand_intf.remote_node.IN_GADAG is false
if L(cand_intf.remote_node) == D(cand_intf.remote_node)
// Special case for cutlinks
cand_intf.UNDIRECTED = false
cand_intf.remote_intf.UNDIRECTED = false
cand_intf.OUTGOING = true
cand_intf.INCOMING = true
cand_intf.remote_intf.OUTGOING = true
cand_intf.remote_intf.INCOMING = true
cand_intf.remote_node.IN_GADAG = true
add_eligible_interfaces_of_node(
ordered_intfs_tree,cand_intf.remote_node)
else
if (cand_intf.remote_node.local_root ==
cand_intf.local_node) &&
check_if_block_has_ear(cand_intf.local_node,
cand_intf.remote_node.block_id))
/* Skip the interface since the block root
already has an incoming interface in the
block */
else
ear_end = SPF_for_Ear(cand_intf.local_node,
cand_intf.remote_node,
cand_intf.remote_node.localroot,
SPF method)
y = ear_end.spf_prev_hop
while y.local_node is not cand_intf.local_node
add_eligible_interfaces_of_node(
ordered_intfs_tree, y.local_node)
y = y.local_node.spf_prev_intf
Figure 33: SPFBased Method for GADAG Construction
Appendix C. Constructing a GADAG Using a Hybrid Method
The idea of this method is to combine the salient features of the
lowpoint inheritance and SPF methods. To this end, we process nodes
as they get added to the GADAG just like in the lowpoint inheritance
by maintaining a stack of nodes. This ensures that we do not need to
maintain lower and higher sets at each node to ascertain ear
directions since the ears will always be directed from the node being
processed towards the end of the ear. To compute the ear however, we
resort to an SPF to have the possibility of better ears (path
lengths) thus giving more flexibility than the restricted use of
lowpoint/dfs parents.
Regarding ears involving a block root, unlike the SPF method, which
ignored interfaces of the block root after the first ear, in the
hybrid method we would have to process all interfaces of the block
root before moving on to other nodes in the block since the direction
of an ear is predetermined. Thus, whenever the block already has an
ear computed, and we are processing an interface of the block root,
we mark the block root as unusable before the SPF run that computes
the ear. This ensures that the SPF terminates at some node other
than the blockroot. This in turn guarantees that the blockroot has
only one incoming interface in each block, which is necessary for
correctly computing the next hops on the GADAG.
As in the SPF GADAG, bridge ears are handled as a special case.
The entire algorithm is shown below in Figure 34.
find_spf_stack_ear(stack, x, y, xy_intf, block_root)
if L(y) == D(y)
// Special case for cutlinks
xy_intf.UNDIRECTED = false
xy_intf.remote_intf.UNDIRECTED = false
xy_intf.OUTGOING = true
xy_intf.INCOMING = true
xy_intf.remote_intf.OUTGOING = true
xy_intf.remote_intf.INCOMING = true
xy_intf.remote_node.IN_GADAG = true
push y onto stack
return
else
if (y.local_root == x) &&
check_if_block_has_ear(x,y.block_id)
//Avoid the block root during the SPF
Mark x as TEMP_UNUSABLE
end_ear = SPF_for_Ear(x,y,block_root,hybrid)
If x was set as TEMP_UNUSABLE, clear it
cur = end_ear
while (cur != y)
intf = cur.spf_prev_hop
prev = intf.local_node
intf.UNDIRECTED = false
intf.remote_intf.UNDIRECTED = false
intf.OUTGOING = true
intf.remote_intf.INCOMING = true
push prev onto stack
cur = prev
xy_intf.UNDIRECTED = false
xy_intf.remote_intf.UNDIRECTED = false
xy_intf.OUTGOING = true
xy_intf.remote_intf.INCOMING = true
return
Construct_GADAG_via_hybrid(topology,root)
Compute_Localroot (root,root)
Assign_Block_ID(root,0)
root.IN_GADAG = true
Initialize Stack to empty
push root onto Stack
while (Stack is not empty)
x = pop(Stack)
for each interface intf of x
y = intf.remote_node
if y.IN_GADAG is false
find_spf_stack_ear(stack, x, y, intf, y.block_root)
Figure 34: Hybrid GADAG Construction Method
Acknowledgements
The authors would like to thank Shraddha Hegde, Eric Wu, Janos
Farkas, Stewart Bryant, Alvaro Retana, and Deccan (Shaofu Peng) for
their suggestions and review. We would also like to thank Anil Kumar
SN for his assistance in clarifying the algorithm description and
pseudocode.
Authors' Addresses
Gabor Sandor Enyedi
Ericsson
Konyves Kalman krt 11
Budapest 1097
Hungary
Email: Gabor.Sandor.Enyedi@ericsson.com
Andras Csaszar
Ericsson
Konyves Kalman krt 11
Budapest 1097
Hungary
Email: Andras.Csaszar@ericsson.com
Alia Atlas
Juniper Networks
10 Technology Park Drive
Westford, MA 01886
United States
Email: akatlas@juniper.net
Chris Bowers
Juniper Networks
1194 N. Mathilda Ave.
Sunnyvale, CA 94089
United States
Email: cbowers@juniper.net
Abishek Gopalan
University of Arizona
1230 E Speedway Blvd.
Tucson, AZ 85721
United States
Email: abishek@ece.arizona.edu

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