{"paper":{"title":"Compact and Fast Sensitivity Oracles for Single-Source Distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Davide Bil\\`o, Guido Proietti, Luciano Gual\\`a, Stefano Leucci","submitted_at":"2016-08-16T20:38:20Z","abstract_excerpt":"Let $s$ denote a distinguished source vertex of a non-negatively real weighted and undirected graph $G$ with $n$ vertices and $m$ edges. In this paper we present two efficient \\emph{single-source approximate-distance sensitivity oracles}, namely \\emph{compact} data structures which are able to \\emph{quickly} report an approximate (by a multiplicative stretch factor) distance from $s$ to any node of $G$ following the failure of any edge in $G$. More precisely, we first present a sensitivity oracle of size $O(n)$ which is able to report 2-approximate distances from the source in $O(1)$ time. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04769","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"}