{"paper":{"title":"Approximate Distance Oracles with Improved Query Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Christian Wulff-Nilsen","submitted_at":"2012-02-10T19:51:10Z","abstract_excerpt":"Given an undirected graph $G$ with $m$ edges, $n$ vertices, and non-negative edge weights, and given an integer $k\\geq 2$, we show that a $(2k-1)$-approximate distance oracle for $G$ of size $O(kn^{1 + 1/k})$ and with $O(\\log k)$ query time can be constructed in $O(\\min\\{kmn^{1/k},\\sqrt km + kn^{1 + c/\\sqrt k}\\})$ time for some constant $c$. This improves the $O(k)$ query time of Thorup and Zwick. Furthermore, for any $0 < \\epsilon \\leq 1$, we give an oracle of size $O(kn^{1 + 1/k})$ that answers $((2 + \\epsilon)k)$-approximate distance queries in $O(1/\\epsilon)$ time. At the cost of a $k$-fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2336","kind":"arxiv","version":3},"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"}