On the Feasibility of Perfect Resilience with Local Fast Failover

TL;DR

This paper investigates the limits and possibilities of achieving perfect network resilience with local fast failover, revealing fundamental impossibility results and proposing efficient algorithms for specific graph classes.

Contribution

It establishes new impossibility results for non-planar graphs and introduces simple failover algorithms for graph families closed under link subdivision, including outerplanar graphs.

Findings

Impossible to achieve perfect resilience on non-planar graphs.

Planarity is necessary but not sufficient for perfect resilience.

Efficient failover algorithms work for certain graph classes like outerplanar graphs.

Abstract

In order to provide a high resilience and to react quickly to link failures, modern computer networks support fully decentralized flow rerouting, also known as local fast failover. In a nutshell, the task of a local fast failover algorithm is to pre-define fast failover rules for each node using locally available information only. These rules determine for each incoming link from which a packet may arrive and the set of local link failures (i.e., the failed links incident to a node), on which outgoing link a packet should be forwarded. Ideally, such a local fast failover algorithm provides a perfect resilience deterministically: a packet emitted from any source can reach any target, as long as the underlying network remains connected. Feigenbaum et al. (ACM PODC 2012) and also Chiesa et al. (IEEE/ACM Trans. Netw. 2017) showed that it is not always possible to provide perfect resilience. Interestingly, not much more is known currently about the feasibility of perfect resilience. This paper revisits perfect resilience with local fast failover, both in a model where the source can and cannot be used for forwarding decisions. We first derive several fairly general impossibility results: By establishing a connection between graph minors and resilience, we prove that it is impossible to achieve perfect resilience on any non-planar graph; furthermore, while planarity is necessary, it is also not sufficient for perfect resilience. On the positive side, we show that graph families closed under link subdivision allow for simple and efficient failover algorithms which simply skip failed links. We demonstrate this technique by deriving perfect resilience for outerplanar graphs and related scenarios, as well as for scenarios where the source and target are topologically close after failures.