{"paper":{"title":"Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Karl Bringmann, Karol W\\k{e}grzycki, Marvin K\\\"unnemann","submitted_at":"2019-07-25T14:14:06Z","abstract_excerpt":"Zwick's $(1+\\varepsilon)$-approximation algorithm for the All Pairs Shortest Path (APSP) problem runs in time $\\widetilde{O}(\\frac{n^\\omega}{\\varepsilon} \\log{W})$, where $\\omega \\le 2.373$ is the exponent of matrix multiplication and $W$ denotes the largest weight. This can be used to approximate several graph characteristics including the diameter, radius, median, minimum-weight triangle, and minimum-weight cycle in the same time bound.\n  Since Zwick's algorithm uses the scaling technique, it has a factor $\\log W$ in the running time. In this paper, we study whether APSP and related problems"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11078","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}