{"paper":{"title":"On the Shoshan-Zwick Algorithm for the All-Pairs Shortest Path Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"K. Subramani, Matthew Williamson, Pavlos Eirinakis","submitted_at":"2016-03-29T03:34:38Z","abstract_excerpt":"The Shoshan-Zwick algorithm solves the all pairs shortest paths problem in undirected graphs with integer edge costs in the range $\\{1, 2, \\dots, M\\}$. It runs in $\\tilde{O}(M\\cdot n^{\\omega})$ time, where $n$ is the number of vertices, $M$ is the largest integer edge cost, and $\\omega < 2.3727$ is the exponent of matrix multiplication. It is the fastest known algorithm for this problem. This paper points out the erroneous behavior of the Shoshan-Zwick algorithm and revises the algorithm to resolve the issues that cause this behavior. Moreover, it discusses implementation aspects of the Shosha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08627","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"}