Single-Source Shortest Paths with Negative Real Weights in $\tilde{O}(mn^{8/9})$ Time
Data Structures and Algorithms
2023-11-14 v2
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 vertices and edges, the algorithm completes in time with high probability. For real-weighted graphs, this result constitutes the first asymptotic improvement over the classic -time algorithm variously attributed to Shimbel, Bellman, Ford, and Moore.
Cite
@article{arxiv.2311.02520,
title = {Single-Source Shortest Paths with Negative Real Weights in $\tilde{O}(mn^{8/9})$ Time},
author = {Jeremy T. Fineman},
journal= {arXiv preprint arXiv:2311.02520},
year = {2023}
}