On the Price of Locality in Static Fast Rerouting

TL;DR

This paper investigates the limitations of local fast rerouting in networks, revealing the inherent trade-offs and conditions under which perfect resilience can or cannot be achieved, especially in restricted graph classes.

Contribution

It characterizes the feasibility of perfect resilience in static fast rerouting, highlighting the high cost of locality and providing impossibility results for certain failure scenarios.

Findings

Local rerouting cannot always find disjoint paths after failures

Impossibility results for perfect resilience with few failures

Insights into resilience on real-world Topology Zoo networks

Abstract

Modern communication networks feature fully decentralized flow rerouting mechanisms which allow them to quickly react to link failures. This paper revisits the fundamental algorithmic problem underlying such local fast rerouting mechanisms. Is it possible to achieve perfect resilience, i.e., to define local routing tables which preserve connectivity as long as the underlying network is still connected? Feigenbaum et al. (ACM PODC'12) and Foerster et al. (SIAM APOCS'21) showed that, unfortunately, it is impossible in general. This paper charts a more complete landscape of the feasibility of perfect resilience. We first show a perhaps surprisingly large price of locality in static fast rerouting mechanisms: even when source and destination remain connected by a linear number of link-disjoint paths after link failures, local rerouting algorithms cannot find any of them which leads to a disconnection on the routing level. This motivates us to study resilience in graphs which exclude certain dense minors, such as cliques or a complete bipartite graphs, and in particular, provide characterizations of the possibility of perfect resilience in different routing models. We provide further insights into the price of locality by showing impossibility results for few failures and investigate perfect resilience on Topology Zoo networks.