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In the Asymmetric k-Center problem, the input is an integer k and a complete digraph over n points together with a distance function obeying the directed triangle inequality. The goal is to choose a set of k points to serve as centers and to assign all the points to the centers, so that the maximum distance of any point to its center is as small as possible.
We show that the Asymmetric k-Center problem is hard to approximate up to a factor of log* n - O(1) unless NP is a subset of or equal to DTIME(nlog log n). Since an O(log* n)-approximation algorithm is known for this problem, this resolves the asymptotic approximability of this problem. This is the first natural problem whose approximability threshold does not polynomially relate to the known approximation classes. We also resolve the approximability threshold of the metric (symmetric) k-Center problem with costs.
approximation algorithms, asymmetric k-center, hardness of approximation, metric k-center
Julia Chuzhoy, Sudipto Guha, Eran Halperin, Sanjeev Khanna, Guy Kortsarz, Robert Krauthgamer, and Joseph Naor, "Asymmetric k-Center is log* n-Hard to Approximate", . June 2004.
Date Posted: 23 September 2004
This document has been peer reviewed.