An Efficient Algorithm for 2D Euclidean 2-Center with Outliers
Computational Geometry
2008-09-13 v2
Abstract
For a set P of n points in R^2, the Euclidean 2-center problem computes a pair of congruent disks of the minimal radius that cover P. We extend this to the (2,k)-center problem where we compute the minimal radius pair of congruent disks to cover n-k points of P. We present a randomized algorithm with O(n k^7 log^3 n) expected running time for the (2,k)-center problem. We also study the (p,k)-center problem in R}^2 under the \ell_\infty-metric. We give solutions for p=4 in O(k^{O(1)} n log n) time and for p=5 in O(k^{O(1)} n log^5 n) time.
Keywords
Cite
@article{arxiv.0806.4326,
title = {An Efficient Algorithm for 2D Euclidean 2-Center with Outliers},
author = {Pankaj K. Agarwal and Jeff M. Phillips},
journal= {arXiv preprint arXiv:0806.4326},
year = {2008}
}
Comments
19 pages, 6 figures. Longer version of paper in ESA08. Adds section on l_\infty (p,k)-center