Shortcutting for Negative-Weight Shortest Path
Abstract
Consider the single-source shortest paths problem on a directed graph with real-valued edge weights. We solve this problem in O(n2.54.5n) 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.
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