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arXiv · 2111.03360

Maintaining Exact Distances under Multiple Edge Failures

Ran Duan·Hanlin Ren
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Abstract

We present the first compact distance oracle that tolerates multiple failures and maintains exact distances. Given an undirected weighted graph $G = (V, E)$ and an arbitrarily large constant $d$, we construct an oracle that given vertices $u, v \in V$ and a set of $d$ edge failures $D$, outputs the exact distance between $u$ and $v$ in $G - D$ (that is, $G$ with edges in $D$ removed). Our oracle has space complexity $O(d n^4)$ and query time $d^{O(d)}$. Previously, there were compact approximate distance oracles under multiple failures [Chechik, Cohen, Fiat, and Kaplan, SODA'17; Duan, Gu, and Ren, SODA'21], but the best exact distance oracles under $d$ failures require essentially $\Omega(n^d)$ space [Duan and Pettie, SODA'09]. Our distance oracle seems to require $n^{\Omega(d)}$ time to preprocess; we leave it as an open question to improve this preprocessing time.

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Ran Duan, Hanlin Ren. 2021-11-05. Maintaining Exact Distances under Multiple Edge Failures. https://arxiv.org/abs/2111.03360

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