Near-Optimal Approximate Decremental All Pairs Shortest Paths

In this paper we consider the decremental approximate all-pairs shortest paths (APSP) problem, where given a graph G the goal is to maintain approximate shortest paths between all pairs of nodes in G under a sequence of online adversarial edge deletions. We present a decremental APSP algorithm for undirected weighted graphs with (2+ε)k-1 stretch, O(m n^1/k +o(1) log(n W)) total update time and O(loglog(n W)) query time for a fixed constant ε, where W is the maximum edge weight (assuming the minimum edge weight is 1) and k is any integer parameter. This is an exponential improvement both in the stretch and in the query time over previous works.

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