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

TL;DR

This paper improves the theoretical lower bound on the number of rewritable bits needed for local failover in directed networks, linking the problem to covering arrays and providing a more precise bound for multiple failures.

Contribution

It introduces a new lower bound for local failover in directed networks by connecting routing success to covering array problems, surpassing previous bounds for multiple failures.

Findings

New lower bound of A6(k + \u23A1\u03BB\, ext{log log}(rac{n}{4}-k)) for k failures in n-node networks

Constructs a network model based on covering arrays to analyze failover capabilities

Shows that more rewritable bits are necessary than previously established for certain network sizes and failure counts.

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.