Approximation Algorithms for the k-center Problem: An Experimental Evaluation

In this paper we deal with the vertex k-center problem, a problem which is a part of the discrete location theory. Informally, given a set of cities, with intercity distances specified, one has to pick k cities and build warehouses in them so as to minimize the maximum distance of any city from its closest warehouse. We examine several approximation algorithms that achieve approximation factor of 2 as well as other heuristic algorithms. In particular, we focus on the clustering algorithm by Gonzalez, the parametric pruning algorithm by Hochbaum-Shmoys, and Shmoys’ algorithm. We discuss several variants of the pure greedy approach. We also describe a new heuristic algorithm for solving the dominating set problem to which the k-center problem is often reduced. We have implemented all the algorithms, experimentally evaluated their quality on 40 standard test graphs in the OR-Lib library, and compared their results with the results found in the recent literature.