Approximation Schemes for Euclidean k-Medians and Related Problems

In the k-median problem we are given a set S of n points in a metric space and a positive integer k. We desire to locate k medians in space, such that the sum of the distances from each of the points of S to the nearest median is minimized. This paper gives an approximation scheme for the plane that for any c > 0 produces a solution of cost at most 1 + 1/c times the optimum and runs in time O(nO(c+1) ). The approximation scheme also generalizes to some problems related to k-median. Our methodology is to extend Arora’s [1, 2] techniques for the TSP, which hitherto seemed inapplicable to problems such as the k-median problem.

• Type: Conference
• Year: 1998
• Where: STOC
• Authors: Sanjeev Arora, Prabhakar Raghavan, Satish Rao
• Keywords: Algorithms, Approximation Scheme, K-median Problem, Positive Integer K, STOC 1998