Asymmetric K-center Is log* H-hard to approximate

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

Research output: Contribution to journalArticlepeer-review


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 from 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 ⊆ DTIME(n log logn). Since an O(log* n)-approximation algorithm is known for this problem, this resolves the asymptotic approximability of ASYMMETRIC k -CENTER. 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.

Original languageEnglish
Pages (from-to)538-551
Number of pages14
JournalJournal of the ACM
Issue number4
StatePublished - 2005
Externally publishedYes


  • Approximation algorithms
  • Asymmetric k-center
  • Hardness of approximation
  • Metric k-center


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