Perfect Network Resilience in Polynomial Time

2026-02-03

AI Summary

This study addresses the problem of achieving perfect source–destination connectivity recovery in communication networks under arbitrary link failures using only local information. To this end, the authors propose a local rerouting mechanism based on priority-based skipping rules and, for the first time, fully characterize the conditions under which perfect resilience is attainable. They further prove that skipping-based rules are expressively equivalent to general local rerouting rules. Leveraging graph-theoretic analysis and algorithmic design, they develop an O(n)-time decision algorithm and an O(nm)-time rule synthesis algorithm, enabling efficient determination of whether a given network supports perfect resilience and automatic generation of the corresponding rerouting strategy. This work substantially advances the theory of distributed fault-tolerant routing.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Modern communication networks support local fast rerouting mechanisms to quickly react to link failures: nodes store a set of conditional rerouting rules which define how to forward an incoming packet in case of incident link failures. The rerouting decisions at any node $v$ must rely solely on local information available at $v$: the link from which a packet arrived at $v$, the target of the packet, and the incident link failures at $v$. Ideally, such rerouting mechanisms provide perfect resilience: any packet is routed from its source to its target as long as the two are connected in the underlying graph after the link failures. Already in their seminal paper at ACM PODC'12, Feigenbaum, Godfrey, Panda, Schapira, Shenker, and Singla showed that perfect resilience cannot always be achieved. While the design of local rerouting algorithms has received much attention since then, we still lack a detailed understanding of when perfect resilience is achievable. This paper closes this gap and presents a complete characterization of when perfect resilience can be achieved. This characterization also allows us to design an $O(n)$-time algorithm to decide whether a given instance is perfectly resilient and an $O(nm)$-time algorithm to compute perfectly resilient rerouting rules whenever it is. Our algorithm is also attractive for the simple structure of the rerouting rules it uses, known as skipping in the literature: alternative links are chosen according to an ordered priority list (per in-port), where failed links are simply skipped. Intriguingly, our result also implies that in the context of perfect resilience, skipping rerouting rules are as powerful as more general rerouting rules. This partially answers a long-standing open question by Chiesa, Nikolaevskiy, Mitrovic, Gurtov, Madry, Schapira, and Shenker [IEEE/ACM Transactions on Networking, 2017] in the affirmative.

Problem

• perfect resilience
• local fast rerouting
• link failures
• network connectivity
• distributed routing

Innovation

• perfect resilience
• local fast rerouting
• skipping rules
• polynomial-time algorithm
• network fault tolerance