English

Robust Proximity Search for Balls using Sublinear Space

Computational Geometry 2014-10-30 v2

Abstract

Given a set of n disjoint balls b1, . . ., bn in IRd, we provide a data structure, of near linear size, that can answer (1 \pm \epsilon)-approximate kth-nearest neighbor queries in O(log n + 1/\epsilon^d) time, where k and \epsilon are provided at query time. If k and \epsilon are provided in advance, we provide a data structure to answer such queries, that requires (roughly) O(n/k) space; that is, the data structure has sublinear space requirement if k is sufficiently large.

Keywords

Cite

@article{arxiv.1401.1472,
  title  = {Robust Proximity Search for Balls using Sublinear Space},
  author = {Sariel Har-Peled and Nirman Kumar},
  journal= {arXiv preprint arXiv:1401.1472},
  year   = {2014}
}
R2 v1 2026-06-22T02:40:41.128Z