Abstract
In this paper we deal with the vertex k-center problem, a problewhich 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.
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Mihelič, J., Robič, B. (2003). Approximation Algorithms for the k-center Problem: An Experimental Evaluation. In: Leopold-Wildburger, U., Rendl, F., Wäscher, G. (eds) Operations Research Proceedings 2002. Operations Research Proceedings 2002, vol 2002. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55537-4_60
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DOI: https://doi.org/10.1007/978-3-642-55537-4_60
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