Asymmetric k-Center is log* n-hard to approximate

Julia Chuzhoy*, Sudipto Guha, Eran Halperin, Sanjeev Khanna, Guy Kortsarz, Joseph Naor

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

18 Scopus citations


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 - ⊖(1) unless NP ⊂ DTIME(nlog log n). Since an O(log* n)-approximation algorithm is known for this problem, this essentially resolves the 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 k-Center problem with costs.

Original languageEnglish
Pages (from-to)21-27
Number of pages7
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
StatePublished - 2004
Externally publishedYes
EventProceedings of the 36th Annual ACM Symposium on Theory of Computing - Chicago, IL, United States
Duration: 13 Jun 200415 Jun 2004


  • Approximation Algorithms
  • Asymmetric k-center
  • Hardness of Approximation
  • Metric k-center


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