Polynomial Time Approximation Schemes for All 1-Center Problems on Metric Rational Set Similarities

In this paper, we investigate algorithms for finding centers of a given collection N of sets. In particular, we focus on metric rational set similarities, a broad class of similarity measures including Jaccard and Hamming. A rational set similarity S is called metric if D= 1 - S is a distance function. We study the 1-center problem on these metric spaces. The problem consists of finding a set C that minimizes the maximum distance of C to any set of N. We present a general framework that computes a (1 + ε) approximation for any metric rational set similarity.