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arXiv · 2311.02520

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

Jeremy T. Fineman
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Abstract

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.

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BibTeXRIS

Jeremy T. Fineman. 2023-11-04. Single-Source Shortest Paths with Negative Real Weights in $\tilde{O}(mn^{8/9})$ Time. https://arxiv.org/abs/2311.02520

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