The multi-service center problem

Abstract

We propose a new type of multiple facilities location problem, called the p-service center problem. In this problem, we are to locate p facilities in the graph, each of which provides distinct service required by all vertices. For each vertex, its p-service distance is the summation of its weighted distances to the p facilities. The objective is to minimize the maximum value among the p-service distances of all vertices. In this paper, we show that the p-service center problem on a general graph is NP-hard, and propose a polynomial-time approximation algorithm. Moreover, we study the basic case p = 2 on paths and trees, and provide linear and near-linear time algorithms. © Springer-Verlag Berlin Heidelberg 2012.