Shortcutting for Negative-Weight Shortest Path

TL;DR

This paper introduces a shortcutting technique that efficiently reduces negative-weight edges in shortest path problems, leading to faster algorithms for dense graphs with real-valued weights.

Contribution

It presents a novel shortcutting method that improves the time complexity for solving single-source shortest paths with negative weights on dense graphs.

Findings

Achieves $O(n^{2.5}\log^{4.5}n)$ time complexity

Outperforms previous algorithms on dense graphs

Introduces a new iterative negative-edge reduction technique

Abstract

Consider the single-source shortest paths problem on a directed graph with real-valued edge weights. We solve this problem in $O(n^{2.5}\log^{4.5}n)$ time, improving on prior work of Fineman (STOC 2024) and Huang-Jin-Quanrud (SODA 2025, 2026) on dense graphs. Our main technique is an shortcutting procedure that iteratively reduces the number of negative-weight edges along shortest paths by a constant factor.