Finding the Largest Disk Containing a Query Point in Logarithmic Time with Linear Storage
Computational Geometry
2013-10-15 v1
Abstract
Let D be a set of n disks in the plane. We present a data structure of size O(n) that can compute, for any query point q, the largest disk in D that contains q, in O(log n) time. The structure can be constructed in O(n log^3 n) time. The optimal storage and query time of the structure improve several recent solutions by Augustine et al. and by Kaplan and Sharir.
Keywords
Cite
@article{arxiv.1310.3388,
title = {Finding the Largest Disk Containing a Query Point in Logarithmic Time with Linear Storage},
author = {Tal Kaminker and Micha Sharir},
journal= {arXiv preprint arXiv:1310.3388},
year = {2013}
}
Comments
15 pages, 9 figures