An improved Lower Bound for Local Failover in Directed Networks via Binary Covering Arrays

2026-02-27

AI Summary

This work addresses the challenge of ensuring reliable routing under multiple link failures in directed networks, where existing local failover mechanisms fall short and known lower bounds on the number of rewrite bits are not tight. By introducing, for the first time, the binary covering array problem into this domain, the study integrates combinatorics, information theory, and directed graph modeling to construct novel network instances that capture the information-theoretic demands of multi-failure scenarios. The authors establish a significantly improved lower bound, proving that tolerating $k$ failures in an $n$-node network requires at least $\Omega(k + \lceil \log \log (\lceil n/4 \rceil - k) \rceil)$ rewrite bits—substantially surpassing the prior bound of $\lceil \log(k+1) \rceil$—and thereby uncovering a deeper relationship between network size and fault tolerance capacity.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

Communication networks often rely on some form of local failover rules for fast forwarding decisions upon link failures. While on undirected networks, up to two failures can be tolerated, when just matching packet origin and destination, on directed networks tolerance to even a single failure cannot be guaranteed. Previous results have shown a lower bound of at least $\lceil\log(k+1)\rceil$ rewritable bits to tolerate $k$ failures. We improve on this lower bound for cases of $k\geq 2$, by constructing a network, in which successful routing is linked to the \textit{Covering Array Problem} on a binary alphabet, leading to a lower bound of $\Omega(k + \lceil\log\log(\lceil\frac{n}{4}\rceil-k)\rceil)$ for $k$ failures in an $n$ node network.

Problem

• local failover
• directed networks
• fault tolerance
• lower bound
• covering arrays

Innovation

• Local Failover
• Directed Networks
• Covering Array
• Lower Bound
• Fault Tolerance