2026-07-23T06:30:49Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:5100 2024-03-06T10:35:53Z ddc:004 open_access

Space Exploration via Proximity Search Har-Peled, Sariel Kumar, Nirman Mount, David M. Raichel, Benjamin Proximity search implicit point set probing We investigate what computational tasks can be performed on a point set in R^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: (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. (B) One can decide if a query point is (approximately) inside the convex-hull of the point set. We also investigate the problem of clustering the given point set, such that meaningful proximity queries can be carried out on the centers of the clusters, instead of the whole point set. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sariel Har-Peled and Nirman Kumar and David M. Mount and Benjamin Raichel 2015 Is Part Of LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SOCG.2015.374 urn:nbn:de:0030-drops-51004 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.374 eng https://creativecommons.org/licenses/by/3.0/legalcode