Space Exploration via Proximity Search

Sariel Har-Peled, Nirman Kumar, David M. Mount, Benjamin Raichel

Research output: Contribution to journalArticlepeer-review


We investigate what computational tasks can be performed on a point set in Rd, 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.

Original languageEnglish (US)
Pages (from-to)357-376
Number of pages20
JournalDiscrete and Computational Geometry
Issue number2
StatePublished - Sep 1 2016


  • Approximation algorithms
  • Clustering
  • Nearest neighbors

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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