{"ID":2843569,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.08551","arxiv_id":"2511.08551","title":"Deterministic Negative-Weight Shortest Paths in Nearly Linear Time via Path Covers","abstract":"We present the first deterministic nearly-linear time algorithm for single-source shortest paths with negative edge weights on directed graphs: given a directed graph $G$ with $n$ vertices, $m$ edges whose weights are integer in $\\{-W,\\dots,W\\}$, our algorithm either computes all distances from a source $s$ or reports a negative cycle in time $\\tilde{O}(m)\\cdot \\log(nW)$ time. All known near-linear time algorithms for this problem have been inherently randomized, as they crucially rely on low-diameter decompositions. To overcome this barrier, we introduce a new structural primitive for directed graphs called the path cover. This plays a role analogous to neighborhood covers in undirected graphs, which have long been central to derandomizing algorithms that use low-diameter decomposition in the undirected setting. We believe that path covers will serve as a fundamental tool for the design of future deterministic algorithms on directed graphs.","short_abstract":"We present the first deterministic nearly-linear time algorithm for single-source shortest paths with negative edge weights on directed graphs: given a directed graph $G$ with $n$ vertices, $m$ edges whose weights are integer in $\\{-W,\\dots,W\\}$, our algorithm either computes all distances from a source $s$ or reports...","url_abs":"https://arxiv.org/abs/2511.08551","url_pdf":"https://arxiv.org/pdf/2511.08551v1","authors":"[\"Bernhard Haeupler\",\"Yonggang Jiang\",\"Thatchaphol Saranurak\"]","published":"2025-11-11T18:32:58Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}