, Volume 61, Issue 1, pp 190–206 | Cite as

Improved Approximation Algorithms for Label Cover Problems

  • Moses Charikar
  • MohammadTaghi Hajiaghayi
  • Howard Karloff


In this paper we consider both the maximization variant Max Rep and the minimization variant Min Rep of the famous Label Cover problem. So far the best approximation ratios known for these two problems were \(O(\sqrt{n})\) and indeed some authors suggested the possibility that this ratio is the best approximation factor for these two problems. We show, in fact, that there are a O(n 1/3)-approximation algorithm for Max Rep and a O(n 1/3log 2/3 n)-approximation algorithm for Min Rep. In addition, we also exhibit a randomized reduction from Densest k-Subgraph to Max Rep, showing that any approximation factor for Max Rep implies the same factor (up to a constant) for Densest k-Subgraph.


Label Cover Approximation algorithm Hardness of approximation Min Rep Max Rep Densest k-Subgraph 


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Copyright information

© Springer Science+Business Media, LLC (outside the USA) 2011

Authors and Affiliations

  • Moses Charikar
    • 1
  • MohammadTaghi Hajiaghayi
    • 2
    • 3
  • Howard Karloff
    • 3
  1. 1.Department of Computer SciencePrinceton UniversityPrincetonUSA
  2. 2.University of Maryland at College ParkCollege ParkUSA
  3. 3.AT&T Labs—ResearchFlorham ParkUSA

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