For a set  P of  n points in i¾?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 i¾?  k points of  P . We present a randomized algorithm with  O ( n  k 7log3 n ) expected running time for the (2, k )-center problem. We also study the ( p , k )-center problem in i¾?2under the i¾? i¾? -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 log5 n ) time.
['Pankaj K. Agarwal', 'Jeff M. Phillips']
An Efficient Algorithm for 2D Euclidean 2-Center with Outliers