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Near-Optimal Decremental SSSP in Dense Weighted Digraphs by Bernstein, Aaron; Gutenberg, Maximilian Probst; Wulff-Nilsen, Christian is a scholarly article available to read on EtoBox.

What is Near-Optimal Decremental SSSP in Dense Weighted Digraphs about?

In the decremental Single-Source Shortest Path problem (SSSP), we are given a weighted directed graph $G=(V,E,w)$ undergoing edge deletions and a source vertex $r \in V$; let $n = |V|, m = |E|$ and $W$ be the aspect ratio of the graph. The goal is to obtain a data structure that maintains shortest paths from $r$ to all vertices in $V$ and can answer distance queries in $O(1)$ time, as well as return the corresponding path $P$ in $O(|P|)$ time. This problem was first considered by Even and Shiloach [JACM'81], who provided an algorithm with total update time $O(mn)$ for unweighted undirected graphs; this was later extended to directed weighted graphs [FOCS'95, STOC'99]. There are conditional lower bounds showing that $O(mn)$ is in fact near-optimal [ESA'04, FOCS'14, STOC'15, STOC'20]. In a breakthrough result, Forster et al. showed that it is possible to achieve total update time $mn^{0.9+o(1)}\log W$ if the algorithm is allowed to return $(1+{\epsilon})$-approximate paths, instead of exact ones [STOC'14, ICALP'15]. No further progress was made until Probst Gutenberg and Wulff-Nilsen [SODA'20] provided a new approach for the problem, which yields total time $\tilde{O}(\min{m^{2/3}n^{

Author

Bernstein, Aaron; Gutenberg, Maximilian Probst; Wulff-Nilsen, Christian

Published

2020

Language

EN