{"ID":2845508,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.04775","arxiv_id":"2511.04775","title":"Improved Additive Approximation Algorithms for APSP","abstract":"The All-Pairs Shortest Paths (APSP) is a foundational problem in theoretical computer science. Approximating APSP in undirected unweighted graphs has been studied for many years, beginning with the work of Dor, Halperin and Zwick [SICOMP'01]. Many recent works have attempted to improve these original algorithms using the algebraic tools of fast matrix multiplication. We improve on these results for the following problems. For $+2$-approximate APSP, the state-of-the-art algorithm runs in $O(n^{2.259})$ time [Dürr, IPL 2023; Deng, Kirkpatrick, Rong, Vassilevska Williams, and Zhong, ICALP 2022]. We give an improved algorithm in $O(n^{2.2255})$ time. For $+4$ and $+6$-approximate APSP, we achieve time complexities $O(n^{2.1462})$ and $O(n^{2.1026})$ respectively, improving the previous $O(n^{2.155})$ and $O(n^{2.103})$ achieved by [Saha and Ye, SODA 2024]. In contrast to previous works, we do not use the big hammer of bounded-difference $(\\min,+)$-product algorithms. Instead, our algorithms are based on a simple technique that decomposes the input graph into a small number of clusters of constant diameter and a remainder of low degree vertices, which could be of independent interest in the study of shortest paths problems. We then use only standard fast matrix multiplication to obtain our improvements.","short_abstract":"The All-Pairs Shortest Paths (APSP) is a foundational problem in theoretical computer science. Approximating APSP in undirected unweighted graphs has been studied for many years, beginning with the work of Dor, Halperin and Zwick [SICOMP'01]. Many recent works have attempted to improve these original algorithms using t...","url_abs":"https://arxiv.org/abs/2511.04775","url_pdf":"https://arxiv.org/pdf/2511.04775v1","authors":"[\"Ce Jin\",\"Yael Kirkpatrick\",\"Michał Stawarz\",\"Virginia Vassilevska Williams\"]","published":"2025-11-06T19:50:31Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}