{"paper":{"title":"Distributed Exact Weighted All-Pairs Shortest Paths in $\\tilde O(n^{5/4})$ Rounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Chien-Chung Huang, Danupon Nanongkai, Thatchaphol Saranurak","submitted_at":"2017-08-13T13:27:47Z","abstract_excerpt":"We study computing {\\em all-pairs shortest paths} (APSP) on distributed networks (the CONGEST model). The goal is for every node in the (weighted) network to know the distance from every other node using communication. The problem admits $(1+o(1))$-approximation $\\tilde O(n)$-time algorithms ~\\cite{LenzenP-podc15,Nanongkai-STOC14}, which are matched with $\\tilde \\Omega(n)$-time lower bounds~\\cite{Nanongkai-STOC14,LenzenP_stoc13,FrischknechtHW12}\\footnote{$\\tilde \\Theta$, $\\tilde O$ and $\\tilde \\Omega$ hide polylogarithmic factors. Note that the lower bounds also hold even in the unweighted cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03903","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"}