{"paper":{"title":"Computing the diameter polynomially faster than APSP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Raphael Yuster","submitted_at":"2010-11-29T10:26:27Z","abstract_excerpt":"We present a new randomized algorithm for computing the diameter of a weighted directed graph. The algorithm runs in $\\Ot(M^{\\w/(\\w+1)}n^{(\\w^2+3)/(\\w+1)})$ time, where $\\w < 2.376$ is the exponent of fast matrix multiplication, $n$ is the number of vertices of the graph, and the edge weights are integers in $\\{-M,...,0,...,M\\}$. For bounded integer weights the running time is $O(n^{2.561})$ and if $\\w=2+o(1)$ it is $\\Ot(n^{7/3})$. This is the first algorithm that computes the diameter of an integer weighted directed graph polynomially faster than any known All-Pairs Shortest Paths (APSP) algo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6181","kind":"arxiv","version":2},"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"}