The textbook algorithm for single-source shortest paths with real-valued edge weights runs in O(mn) time on a graph with m edges and n vertices. A recent breakthrough algorithm by Fineman [Fin24] takes O~(mn8/9) randomized time. We present an O~(mn4/5) randomized time algorithm building on ideas from [Fin24].
@article{arxiv.2407.04872,
title = {Faster single-source shortest paths with negative real weights via proper hop distance},
author = {Yufan Huang and Peter Jin and Kent Quanrud},
journal= {arXiv preprint arXiv:2407.04872},
year = {2024}
}