{"paper":{"title":"Faster Approximate Distance Queries and Compact Routing in Sparse Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.NI","cs.SI"],"primary_cat":"cs.DS","authors_text":"P. Brighten Godfrey, Rachit Agarwal, Sariel Har-Peled","submitted_at":"2012-01-12T23:03:18Z","abstract_excerpt":"A distance oracle is a compact representation of the shortest distance matrix of a graph. It can be queried to approximate shortest paths between any pair of vertices. Any distance oracle that returns paths of worst-case stretch (2k-1) must require space $\\Omega(n^{1 + 1/k})$ for graphs of n nodes. The hard cases that enforce this lower bound are, however, rather dense graphs with average degree \\Omega(n^{1/k}).\n  We present distance oracles that, for sparse graphs, substantially break the lower bound barrier at the expense of higher query time. For any 1 \\leq \\alpha \\leq n, our distance oracl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2703","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"}