{"paper":{"title":"Fast approximation algorithms for $p$-centres in large $\\delta$-hyperbolic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"cs.DS","authors_text":"Iraj Saniee, Katherine Edwards, W. Sean Kennedy","submitted_at":"2016-04-25T18:39:25Z","abstract_excerpt":"We provide a quasilinear time algorithm for the $p$-center problem with an additive error less than or equal to 3 times the input graph's hyperbolic constant. Specifically, for the graph $G=(V,E)$ with $n$ vertices, $m$ edges and hyperbolic constant $\\delta$, we construct an algorithm for $p$-centers in time $O(p(\\delta+1)(n+m)\\log(n))$ with radius not exceeding $r_p + \\delta$ when $p \\leq 2$ and $r_p + 3\\delta$ when $p \\geq 3$, where $r_p$ are the optimal radii. Prior work identified $p$-centers with accuracy $r_p+\\delta$ but with time complexity $O((n^3\\log n + n^2m)\\log(diam(G)))$ which is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07359","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"}