Internet Engineering Task Force S. Chen
Internet-Draft T. Li
Intended status: Informational Arista Networks
Expires: 4 September 2020 3 March 2020
An Algorithm for Computing Dynamic Flooding Topologies
draft-chen-lsr-dynamic-flooding-algorithm-00
Abstract
Link-state routing protocols suffer from excessive flooding in dense
network topologies. Dynamic flooding [I-D.ietf-lsr-dynamic-flooding]
alleviates the problem by decoupling the flooding topology from the
physical topology. Link-state protocol updates are flooded only on
the sparse flooding topology while data traffic is still forwarded on
the physical topology.
This document describes an algorithm to obtain a sparse subgraph from
a dense graph. The resulting subgraph has certain desirable
properties and can be used as a flooding topology in dynamic
flooding.
This document discloses the algorithm that we have developed in order
to make it easier for other developers to implement similar
algorithms. We do not claim that our algorithm is optimal, rather it
is a pragmatic effort and we expect that further research and
refinement can improve the results.
We are not proposing that this algorithm be standardized, nor that
the working group use this as a basis for further standardization
work, however we have no objections if the working group chooses to
do so.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at https://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
Chen & Li Expires 4 September 2020 [Page 1]
Internet-Draft Dynamic Flooding Algorithm March 2020
This Internet-Draft will expire on 4 September 2020.
Copyright Notice
Copyright (c) 2020 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents (https://trustee.ietf.org/
license-info) in effect on the date of publication of this document.
Please review these documents carefully, as they describe your rights
and restrictions with respect to this document. Code Components
extracted from this document must include Simplified BSD License text
as described in Section 4.e of the Trust Legal Provisions and are
provided without warranty as described in the Simplified BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Problem Statement . . . . . . . . . . . . . . . . . . . . . . 3
3. Algorithm Outline . . . . . . . . . . . . . . . . . . . . . . 3
4. Algorithm Details . . . . . . . . . . . . . . . . . . . . . . 4
4.1. Initial Cycle Setup . . . . . . . . . . . . . . . . . . . 4
4.2. Arc Path Selection . . . . . . . . . . . . . . . . . . . 5
4.3. Exceptions . . . . . . . . . . . . . . . . . . . . . . . 6
4.4. LANs . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
6. Security Considerations . . . . . . . . . . . . . . . . . . . 9
7. Informative References . . . . . . . . . . . . . . . . . . . 9
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 9
1. Introduction
In [I-D.ietf-lsr-dynamic-flooding], dynamic flooding is proposed to
reduce the flooding of link-state protocol packets in the network.
The basic idea is to find a sparse flooding topology from the
physical topology and flood link-state protocol data units (LSPDUs or
LSPs) only on the flooding topology. The flooding topology should
have the following properties:
1. It should include all nodes in the area. This ensures that LSPs
can reach all nodes.
2. It should be biconnected if possible. This ensures that the LSP
delivery is resilient to a single node or link failure.
3. It has a limited diameter. Being a subgraph, the flooding
topology often has a larger diameter than the physical topology.
Chen & Li Expires 4 September 2020 [Page 2]
Internet-Draft Dynamic Flooding Algorithm March 2020
A larger diameter indicates a longer convergence time. The
tradeoff between flooding reduction and convergence should be
considered during the flooding topology computation.
4. It has a balanced degree of distribution. The degree of a node
on the flooding topology indicates its burden in flooding LSPs.
It is desirable to balance this burden across multiple nodes.
Hence, the degree of each node should also be considered during
flooding topology computation.
With the above properties in mind, we propose an iterative algorithm
to compute the flooding topology.
2. Problem Statement
We model the physical topology as an undirected graph. Each system
or pseudonode in the area is represented by a node in the graph. An
edge connects two nodes who advertise each other as neighbors. Given
the set of the nodes and the set of edges, we propose an algorithm to
compute a biconnected (if possible) subgraph that covers all nodes.
The subgraph is computed with consideration of diameter and node
degree.
3. Algorithm Outline
A simple cycle that covers all nodes is a biconnected subgraph with
balanced node degrees. While it has some desirable properties, a
simple cycle is not suitable as a flooding topology at large scale.
With N nodes in the area, a link-state update has to take N/2 hops to
reach all nodes. The undue propagation delay causes a long
convergence time.
The proposed algorithm constructs a subgraph composed of small
overlapping cycles. The base graph is denoted by G(V, E), where V is
the set of all reachable nodes in this area, and E is the set of
edges. The subgraph to be computed is denoted by G'({}, {}), which
starts with an empty set of nodes and an empty set of edges.
1. Select a subset of nodes V(0) from V and a subset of edges E(0)
from E to form an initial cycle. This cycle is added to the
subgraph: G'(V(0), E(0)).
2. Select a subset of nodes V(i) and a subset of edges E(i), that
are not included in the current subgraph. That is, V(i) is
selected from V - V(0) - ... - V(i-1) and E(i) is selected from E
- E(0) - ... - E(i-1). These nodes and the edges are selected to
form an arc path whose two endpoints are included in the current
Chen & Li Expires 4 September 2020 [Page 3]
Internet-Draft Dynamic Flooding Algorithm March 2020
subgraph. This arc path is added to the subgraph: G'( V(0) +
V(1) + ... + V(i), E(0) + E(1) + ... + E(i) ).
3. Repeat step 2 until all nodes are included in the subgraph G'.
The subgraph constructed by this algorithm has the following
properties:
1. It covers all nodes in the area.
2. It is biconnected. This can be easily proven by induction.
Specifically, the initial cycle is biconnected. Adding an arc
path, whose two endpoints differ, to a biconnected subgraph
maintains the biconnectivity of the subgraph.
3. It has a limited diameter. By selecting small cycles, the
subgraph will have a smaller diameter. More specifically, the
implementation can pick endpoints of each arc path to reduce the
diameter of the subgraph. The degree of a node in the subgraph
is determined by the number of arc paths it is on. By carefully
selecting the arc endpoints, we may balance the node degrees.
Together with the encoding scheme in [I-D.ietf-lsr-dynamic-flooding],
this algorithm can be used to implement centralized dynamic flooding.
The area leader can build the base graph from its link-state database
(LSDB), apply this algorithm to compute the flooding topology, and
then encode it into the Dynamic Flooding Path TLVs specified in
[I-D.ietf-lsr-dynamic-flooding]. In a topology change event, the
area leader can repeat the above process and send out the new
flooding topology.
4. Algorithm Details
The outlined algorithm allows for different approaches to find the
initial cycle and subsequent arc paths. We do not intend to find the
theoretically optimal solution. Our aim is to find a practical
approach that works for any connected base graph, and is also easy to
implement.
4.1. Initial Cycle Setup
The initial cycle forms a base of the subgraph computation.
Intuitively, we would like to place the initial cycle around the
centroid of the base graph, and gradually expand it outwards.
Complicated graph analysis can help, but is not desired.
We propose to select a starting node and then search a path that ends
at this node. We suggest selecting the node with the highest degree
Chen & Li Expires 4 September 2020 [Page 4]
Internet-Draft Dynamic Flooding Algorithm March 2020
as the starting node. The degree of each node can be easily
determined when the base graph is constructed from the LSDB.
Starting from this node, we perform a depth-first search (DFS) for a
limited number of steps, and then a breadth-first search (BFS) to
find the shortest path back to the starting node. The restriction of
the DFS depths and the use of BFS effectively help limit the diameter
of the initial cycle. Below is a summary of the procedure. We omit
the details of the well-known DFS and BFS algorithms.
1. Let V(0) = [] be the list of nodes on the initial cycle.
2. Find the starting node, denoted by n0. V(0) = [n0].
3. Perform DFS starting from n0 until either the first leaf is
reached or the depth exceeds a preset limit. The visited nodes
are denoted by n1, n2, ..., ni, where i < DFS depth limit, and
added to the list V(0) in order.
4. Mark nodes in V(0) as visited to avoid BFS visiting these nodes.
Then perform BFS to find the shortest path from ni to n0. Append
nodes on the shortest path to V(0). Since this is a cycle, node
n0 appears twice in V(0): the first and the last places.
Note that since DFS and BFS do not process a node more than once, we
are ensured to obtain a cycle (if one exists) from the above
procedure.
4.2. Arc Path Selection
After obtaining an initial cycle, we recursively add arc paths to the
subgraph until all nodes are included. Each arc path's two endpoints
are chosen from the current subgraph. This ensures that the
resulting subgraph remains biconnected. To limit the diameter of the
resulting subgraph, we select an arc path with limited length and
attach it closer to the initial cycle.
In each iteration, we have a starting subgraph, which includes the
initial cycle and the arc paths obtained in earlier iterations. We
first select a node from the starting subgraph, that has at least one
neighbor that is not in the starting subgraph. To balance the degree
distribution, we prefer to select a node that has the least degree in
the starting subgraph. Meanwhile, we intend to place the new arc
path closer to the initial cycle, which will help reduce the diameter
of the resulting subgraph. As the number of iterations increases, it
becomes hard to find such nodes that meet both conditions. A
tradeoff between the node degree and the node distance to the initial
cycle has to be made.
Chen & Li Expires 4 September 2020 [Page 5]
Internet-Draft Dynamic Flooding Algorithm March 2020
Starting from the selected node, we perform a DFS for a limited
number of steps in the base graph to include nodes and edges that do
not belong to the starting subgraph. Then BFS is performed to find
the shortest path back to any node in the starting subgraph except
the starting node of this iteration. The resulting path is combined
with the starting subgraph to generate a new subgraph, which serves
as the starting subgraph in the next iteration. The iteration is
repeated until all nodes in the base graph are included in the
subgraph.
The procedure in each iteration is very similar to the one used to
find the initial cycle, except that the two endpoints of the new path
do not match:
1. Let V(i) = [] be the list of nodes found in the i-th iteration.
The starting subgraph includes nodes in V(0) + ... + V(i-1), and
edges between each pair of adjacent nodes in each node list V(j).
2. Select a starting node n0 for this iteration from the starting
subgraph. V(i) = [n0].
3. Mark all nodes in V(0) + ... + V(i-1) as visited. Then perform
DFS from n0 until either the first leaf is reached or the depth
exceeds a preset limit. Nodes visited in this iteration are
denoted by n1, n2, ..., ni in order, and appended to the list
V(i).
4. Mark all nodes in V(0) + ... + V(i-1) + V(i) as visited. Then
perform BFS to find the shortest path from ni to any node in V(0)
+ ... V(i-1) - [n0], where n0 is the starting node in this
iteration. If a path is found, append its nodes to V(i) and
repeat the iteration from step 1.
By correctly marking the visited nodes before DFS and BFS, we ensure
that the obtained arc path (if it exists) has two endpoints and only
these two points on the starting subgraph.
4.3. Exceptions
If the base graph is biconnected, there exists a simple cycle between
any two nodes. We are thus ensured to find one arc path in each
iteration and the algorithm described above will yield a biconnected
subgraph that covers all nodes in the base graph. Otherwise,
however, we may not be able to find an arc path with both endpoints
belonging to the starting subgraph in that iteration. When this
happens, we know that the edge between the last node found by DFS and
its parent is a cut edge in the base graph. For connectivity, this
edge must be included in the resulting subgraph. Hence, when step 4
Chen & Li Expires 4 September 2020 [Page 6]
Internet-Draft Dynamic Flooding Algorithm March 2020
(the BFS stage in earlier procedures) fails, we should amend it with
the following:
5. If BFS does not find a shortest path from ni, and V(i) contains
only two nodes, i.e., the cut edge case, then go back to step 1
to continue the iteration.
6. If BFS does not find a shortest path from ni, and V(i) contains
more than two nodes, then remove the last node from V(i), and go
back to step 4.
Similarly, we might face the same problem when selecting the initial
cycle. We can apply step 6 until we find a cycle. However, if we
happen to find a cut edge, we can change the first neighbor of the
starting node that is visited by the DFS and repeat the procedure.
If all edges connecting to the starting node are cut edges, we can
change the starting node. If an initial cycle is not found after all
the above efforts, indicating that the base graph does not have a
cycle, then we will return the base graph as the result.
4.4. LANs
We model a pseudonode as a node in the base graph. The proposed
algorithm can be applied as-is. There are, however, possible
optimizations for the multi-access LAN case. First, a pseudonode is
not required to be on the flooding topology. The algorithm can thus
be terminated as soon as all real nodes are included in the subgraph.
Second, if a pseudonode is included on the flooding topology, all
nodes connecting to this LAN will have to flood their LSPs to this
LAN (see [I-D.ietf-lsr-dynamic-flooding] Section 6.6). Hence, if a
pseudonode is included in the subgraph, then it will automatically
provide uni-connectivity to all its neighbors that are not yet
included. The algorithm can take advantage of this LAN property to
reduce the edges in the subgraph.
5. Example
The proposed algorithm can be applied to any connected base graph.
For ease of explanation, we consider a complete graph of 10 nodes and
45 edges. To limit the diameter of the resulting subgraph, we pre-
set the maximum steps in the DFS to 3.
1. Let ni, i = 0, 1, ... 9, denote nodes in the base graph.
2. Find an initial cycle.
a. Without loss of generality, we select node n0 as the starting
point.
Chen & Li Expires 4 September 2020 [Page 7]
Internet-Draft Dynamic Flooding Algorithm March 2020
b. Perform DFS from n0 for 3 steps. We obtain a path n0 - n1 -
n2 - n3.
c. Perform BFS from n3 to n0. Since this is a complete graph,
where every node is directly connected to any other node, the
shortest path is only one hop away.
d. The initial cycle is found n0 - n1 - n2 - n3 - n0.
3. Find the first arc path.
a. Select a node on the initial cycle, say n0.
b. Perform DFS from n0 for 3 steps. We obtain a path n0 - n4 -
n5 - n6.
c. Perform BFS from n6 to any node on the initial cycle except
n0, i.e., {n1, n2, n3}. These three nodes have the same
degree. We may select any one of them as the endpoint.
Suppose that n1 is selected.
d. The first arc path is found n0 - n4 - n5 - n6 - n1.
4. Find the second arc path.
a. When selecting the starting node for this path, we may
consider the current node degree as well as the node distance
to n0 (the starting point of the initial cycle). We notice
that both n0 and n1 have a degree of 3 while other nodes have
a degree of 2. Nodes n1, n3, n4 are the closest to n0. We
select a node with a lower degree and closer to n0. Suppose
n3 is selected.
b. Perform DFS from n3 for 3 steps. We obtain a path n3 - n7
-n8 - n9.
c. Perform BFS from n9 to any node except n3. Using the same
criteria in a. to select the endpoint, we select n4.
d. The second arc path is found n3 - n7 -n8 - n9 - n4.
5. The subgraph has included all nodes. The iteration ends.
The subgraph found by the proposed algorithm can be represented by
three paths:
n0 - n1 - n2 - n3 - n0
Chen & Li Expires 4 September 2020 [Page 8]
Internet-Draft Dynamic Flooding Algorithm March 2020
n0 - n4 - n5 - n6 - n1
n3 - n7 -n8 - n9 - n4
The subgraph has 12 edges, significantly reduced from 45 in the base
graph. The highest node degree is 3 and the lowest node degree is 2.
The diameter of the subgraph is 4, increased, as expected, from that
of the base graph.
6. Security Considerations
This document introduces no new security issues. Security issues
within dynamic flooding are already discussed in
[I-D.ietf-lsr-dynamic-flooding].
7. Informative References
[I-D.ietf-lsr-dynamic-flooding]
Li, T., Psenak, P., Ginsberg, L., Chen, H., Przygienda,
T., Cooper, D., Jalil, L., and S. Dontula, "Dynamic
Flooding on Dense Graphs", Work in Progress, Internet-
Draft, draft-ietf-lsr-dynamic-flooding-04, 26 November
2019, .
Authors' Addresses
Sarah Chen
Arista Networks
5453 Great America Parkway
Santa Clara, California 95054
United States of America
Email: sarahchen@arista.com
Tony Li
Arista Networks
5453 Great America Parkway
Santa Clara, California 95054
United States of America
Email: tony.li@tony.li
Chen & Li Expires 4 September 2020 [Page 9]