{"paper":{"title":"Computing the k Nearest-Neighbors for all Vertices via Dijkstra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Sariel Har-Peled","submitted_at":"2016-07-26T17:49:46Z","abstract_excerpt":"We are given a directed graph $G = (V,E)$ with $n$ vertices and $m$ edges, with positive weights on the edges, and a parameter $k >0$. We show how to compute, for every vertex $v \\in V$, its $k$ nearest-neighbors. The algorithm runs in $O( k ( n \\log n + m ) )$ time, and follows by a somewhat careful modification of Dijkstra's shortest path algorithm.\n  This result is probably folklore, but we were unable to find a reference to it -- thus, this note."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07818","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"}