Faster single-source shortest paths with negative real weights via proper hop distance

TL;DR

This paper introduces a faster randomized algorithm for single-source shortest paths with real weights, improving the runtime from previous methods by leveraging new algorithmic ideas.

Contribution

It presents an $ ilde O(m n^{4/5})$ randomized algorithm for shortest paths with negative real weights, advancing the state-of-the-art in algorithm efficiency.

Findings

Achieves faster runtime than previous algorithms

Builds on recent breakthroughs in shortest path algorithms

Uses novel techniques to improve computational complexity

Abstract

The textbook algorithm for single-source shortest paths with real-valued edge weights runs in $O(m n)$ time on a graph with $m$ edges and $n$ vertices. A recent breakthrough algorithm by Fineman [Fin24] takes $\tilde O(m n^{8/9})$ randomized time. We present an $\tilde O(m n^{4/5})$ randomized time algorithm building on ideas from [Fin24].