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arXiv · 2110.11613

Pairwise Reachability Oracles and Preservers under Failures

Diptarka Chakraborty·Kushagra Chatterjee·Keerti Choudhary
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Abstract

In this paper, we consider reachability oracles and reachability preservers for directed graphs/networks prone to edge/node failures. Let $G = (V, E)$ be a directed graph on $n$-nodes, and $P\subseteq V\times V$ be a set of vertex pairs in $G$. We present the first non-trivial constructions of single and dual fault-tolerant pairwise reachability oracle with constant query time. Furthermore, we provide extremal bounds for sparse fault-tolerant reachability preservers, resilient to two or more failures. Prior to this work, such oracles and reachability preservers were widely studied for the special scenario of single-source and all-pairs settings. However, for the scenario of arbitrary pairs, no prior (non-trivial) results were known for dual (or more) failures, except those implied from the single-source setting. One of the main questions is whether it is possible to beat the $O(n |P|)$ size bound (derived from the single-source setting) for reachability oracle and preserver for dual failures (or $O(2^k n|P|)$ bound for $k$ failures). We answer this question affirmatively.

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Diptarka Chakraborty, Kushagra Chatterjee, Keerti Choudhary. 2021-10-22. Pairwise Reachability Oracles and Preservers under Failures. https://arxiv.org/abs/2110.11613

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