Fully Dynamic Shortest Paths in Sparse Digraphs

Abstract

We study the exact fully dynamic shortest paths problem. For real-weighted directed graphs, we show a deterministic fully dynamic data structure with $\tilde{O}(m{n}^{4/5})$ worst-case update time processing arbitrary $s,t$-distance queries in $\tilde{O}(n^{4/5})$ time. This constitutes the first non-trivial update/query tradeoff for this problem in the regime of sparse weighted directed graphs.

This paper describes the main contribution of our ICALP 2023 paper (see DOI). In addition to the current result, the ICALP 2023 paper also claimed a secondary result on fully dynamic reachability in general sparse digraphs that is flawed. This version retracts that claim and contains a discussion of the error. We thank Jan van den Brand for pointing out this issue