Approximation Algorithms for Geometric Median Problems

Abstract

In this paper we present approximation algorithms for median problems in metric spaces and xed-dimensional Euclidean space. Our algorithms use a new method for transforming an optimal solution of the linear program relaxation of the s-median problem into a provably good integral solution. This transfor- mation technique is fundamentally di erent from the methods of randomized and deterministic rounding [Rag, RaT] and the methods proposed in [LiV] in the following way: Previous techniques never set variables with zero values in the fractional solution to 1. This departure from previous methods is crucial for the success of our algorithms.