An Efficient Algorithm for 2D Euclidean 2-Center with Outliers

For a set P of n points in R2 , 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(nk7 log3 n) expected running time for the (2, k)-center problem. We also study the (p, k)-center problem in R2 under the -metric. We give solutions for p = 4 in O(kO(1) n log n) time and for p = 5 in O(kO(1) n log5 n) time.

• Type: Conference
• Year: 2008
• Where: ESA
• Authors: Pankaj K. Agarwal, Jeff M. Phillips
• Keywords: Algorithms, Congruent Disks, ESA 2008, K)-center Problem, Minimal Radius