Complexity of Perfect and Ideal Resilience Verification in Fast Re-Route Networks

2026-01-07

arXiv.org

AI Summary

This study investigates whether decentralized fast rerouting mechanisms can achieve perfect or ideal resilience—ensuring uninterrupted communication between connected nodes—under link failures. Focusing on rerouting schemes that rely solely on local static rules, the work establishes for the first time that the problem of verifying such resilience is coNP-complete, thereby determining a fundamental lower bound on its theoretical complexity. For a simplified model without ingress port information, the authors further develop a linear-time algorithm for both verification and synthesis of resilient routing policies. By integrating computational complexity theory, graph theory, and formal methods, this research provides crucial theoretical foundations and efficient practical tools for the design of highly reliable networks.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic 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

To achieve fast recovery from link failures, most modern communication networks feature fully decentralized fast re-routing mechanisms. These re-routing mechanisms rely on pre-installed static re-routing rules at the nodes (the routers), which depend only on local failure information, namely on the failed links incident to the node. Ideally, a network is perfectly resilient: the re-routing rules ensure that packets are always successfully routed to their destinations as long as the source and the destination are still physically connected in the underlying network after the failures. Unfortunately, there are examples where achieving perfect resilience is not possible. Surprisingly, only very little is known about the algorithmic aspect of when and how perfect resilience can be achieved. We investigate the computational complexity of analyzing such local fast re-routing mechanisms. Our main result is a negative one: we show that even checking whether a given set of static re-routing rules ensures perfect resilience is coNP-complete. We also show coNP-completeness of the so-called ideal resilience, a weaker notion of resilience often considered in the literature. Additionally, we investigate other fundamental variations of the problem. In particular, we show that our coNP-completeness proof also applies to scenarios where the re-routing rules have specific patterns (known as skipping in the literature). On the positive side, for scenarios where nodes do not have information about the link from which a packet arrived (the so-called in-port), we present linear-time algorithms for both the verification and synthesis problem for perfect resilience.

Problem

• perfect resilience
• ideal resilience
• fast re-route
• computational complexity
• network verification

Innovation

• perfect resilience
• fast re-route
• computational complexity
• coNP-completeness
• in-port oblivious