English

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 nn vertices and mm edges, the algorithm completes in O~(mn8/9)\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)O(mn)-time algorithm variously attributed to Shimbel, Bellman, Ford, and Moore.

Keywords

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}
}
R2 v1 2026-06-28T13:11:44.644Z