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Local Fast Rerouting with Low Congestion: A Randomized Approach

Gregor Bankhamer, Robert Elsässer, Stefan Schmid

TL;DR

This paper presents local fast rerouting algorithms which not only provide a high degree of resilience against multiple link failures, but also ensure a low congestion on the resulting failover paths.

Abstract

Most modern communication networks include fast rerouting mechanisms, implemented entirely in the data plane, to quickly recover connectivity after link failures. By relying on local failure information only, these data plane mechanisms provide very fast reaction times, but at the same time introduce an algorithmic challenge in case of multiple link failures: failover routes need to be robust to additional but locally unknown failures downstream. This paper presents local fast rerouting algorithms which not only provide a high degree of resilience against multiple link failures, but also ensure a low congestion on the resulting failover paths. We consider a randomized approach and focus on networks which are highly connected before the failures occur. Our main contribution are three simple algorithms which come with provable guarantees and provide interesting resilience-load tradeoffs, significantly outperforming any deterministic fast rerouting algorithm with high probability.

Local Fast Rerouting with Low Congestion: A Randomized Approach

TL;DR

This paper presents local fast rerouting algorithms which not only provide a high degree of resilience against multiple link failures, but also ensure a low congestion on the resulting failover paths.

Abstract

Most modern communication networks include fast rerouting mechanisms, implemented entirely in the data plane, to quickly recover connectivity after link failures. By relying on local failure information only, these data plane mechanisms provide very fast reaction times, but at the same time introduce an algorithmic challenge in case of multiple link failures: failover routes need to be robust to additional but locally unknown failures downstream. This paper presents local fast rerouting algorithms which not only provide a high degree of resilience against multiple link failures, but also ensure a low congestion on the resulting failover paths. We consider a randomized approach and focus on networks which are highly connected before the failures occur. Our main contribution are three simple algorithms which come with provable guarantees and provide interesting resilience-load tradeoffs, significantly outperforming any deterministic fast rerouting algorithm with high probability.

Paper Structure

This paper contains 24 sections, 23 theorems, 21 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Model in a Nutshell
  3. The Deterministic Case Lower Bound
  4. Our Results
  5. Further Related Work
  6. Model
  7. Beating Deterministic Approaches with Three Permutations
  8. Notation and Conventions
  9. Analysis
  10. Measuring Forests
  11. Accounting for Inner Edge Failures
  12. From Forests to Load
  13. Circumventing Cycles by Partitioning
  14. Analysis
  15. Cycles
  16. ...and 9 more sections

Key Result

Theorem 1

Assume that the adversary fails at most $\alpha \cdot n$ edges where $\alpha <1$ is a non-negative constantMore specifically, $\alpha$ can be an arbitrary constant with $0 < \alpha < (n-1) / n$. Note that this upper-bound quickly tends towards $1$ for large $n$.. Then, if all nodes perform all-to-on flows passes at all but $O(\log^2 n)$ nodes. Furthermore, all remaining nodes, except for $d$, rece

Figures (8)

  • Figure 1: All-to-one routing in the complete graph $K_5$. Each node sends one flow towards destination $d$, each corresponding to one of the colored lines in non-solid style. Because the link $(u,d)$ is failed the flow of $u$ needs to take a detour. This causes the edge $(v,d)$ to accumulate a load of 2.
  • Figure 2: 3-Permutations protocol. Point-of-view of some node $v$
  • Figure 3: The structures contained in the subgraph $G'$. On the left, a tree rooted in some $v \in V_G$ is presented. On the right, we have a cycle and each node of the cycle is again the root root of a tree.
  • Figure 4: For some node $v$ the edge $(v, \pi_v^{(i)} (1))$ is failed (marked in red). In $G"(i)$ this edge is replaced by $(v, \pi_v^{(j)})$, causing the subtree rooted in $v$ to relocate.
  • Figure 5: Intervals protocol. Point-of-view of some node $v$
  • ...and 3 more figures

Theorems & Definitions (24)

  • Theorem 1
  • Definition 1: Inner/Destination Edges and Good/Bad Nodes
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Corollary 1
  • Lemma 4
  • Lemma 5
  • Corollary 2
  • Lemma 6
  • ...and 14 more