{"paper":{"title":"On the complexity of the (approximate) nearest colored node problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Maximilian Probst","submitted_at":"2018-07-10T15:46:41Z","abstract_excerpt":"Given a graph $G=(V,E)$ where each vertex is assigned a color from the set $C=\\{c_1, c_2, .., c_\\sigma\\}$. In the (approximate) nearest colored node problem, we want to query, given $v \\in V$ and $c \\in C$, for the (approximate) distance $\\widehat{\\mathbf{dist}}(v, c)$ from $v$ to the nearest node of color $c$. For any integer $1 \\leq k \\leq \\log n$, we present a Color Distance Oracle (also often referred to as Vertex-label Distance Oracle) of stretch $4k-5$ using space $O(kn\\sigma^{1/k})$ and query time $O(\\log{k})$. This improves the query time from $O(k)$ to $O(\\log{k})$ over the best known"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03721","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"}