Shortcutting for Negative-Weight Shortest Path
By: George Z. Li , Jason Li , Satish Rao and more
Potential Business Impact:
Finds fastest routes in complex networks faster.
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.
Similar Papers
From Hop Reduction to Sparsification for Negative Length Shortest Paths
Data Structures and Algorithms
Finds shortest paths faster, even with negative costs.
From Hop Reduction to Sparsification for Negative Length Shortest Paths
Data Structures and Algorithms
Finds shortest paths faster, even with bad steps.
Faster Negative-Weight Shortest Paths and Directed Low-Diameter Decompositions
Data Structures and Algorithms
Finds shortest paths faster in tricky networks.