{"paper":{"title":"Space Exploration via Proximity Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Benjamin Raichel, David M. Mount, Nirman Kumar, Sariel Har-Peled","submitted_at":"2014-12-03T16:51:03Z","abstract_excerpt":"We investigate what computational tasks can be performed on a point set in $\\Re^d$, if we are only given black-box access to it via nearest-neighbor search. This is a reasonable assumption if the underlying point set is either provided implicitly, or it is stored in a data structure that can answer such queries. In particular, we show the following:\n(A) One can compute an approximate bi-criteria $k$-center clustering of the point set, and more generally compute a greedy permutation of the point set. \n(B) One can decide if a query point is (approximately) inside the convex-hull of the point set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1398","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"}