Single-Source Shortest Paths with Negative Real Weights in $\tilde{O}(mn^{8/9})$ Time

This paper presents a randomized algorithm for the problem of single-source shortest paths on directed graphs with real (both positive and negative) edge weights. Given an input graph with $n$ vertices and $m$ edges, the algorithm completes in $\tilde{O}(mn^{8/9})$ time with high probability. For re...

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Bibliographic Details
Main Author Fineman, Jeremy T
Format Journal Article
LanguageEnglish
Published 04.11.2023
Subjects
Computer Science - Data Structures and Algorithms
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Summary:This paper presents a randomized algorithm for the problem of single-source shortest paths on directed graphs with real (both positive and negative) edge weights. Given an input graph with $n$ vertices and $m$ edges, the algorithm completes in $\tilde{O}(mn^{8/9})$ time with high probability. For real-weighted graphs, this result constitutes the first asymptotic improvement over the classic $O(mn)$-time algorithm variously attributed to Shimbel, Bellman, Ford, and Moore.
DOI:10.48550/arxiv.2311.02520