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.
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}
}