Maintaining Exact Distances under Multiple Edge Failures

11/05/2021

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by   Ran Duan, et al.

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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 ∈ 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 Ω(n^d) space [Duan and Pettie, SODA'09]. Our distance oracle seems to require n^Ω(d) time to preprocess; we leave it as an open question to improve this preprocessing time.