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computational complexity

, Volume 15, Issue 1, pp 20–39 | Cite as

On the complexity of approximating k-set packing

  • Elad Hazan
  • Shmuel Safra
  • Oded Schwartz
Original Paper

Abstract.

Given a k-uniform hypergraph, the Maximum k -Set Packing problem is to find the maximum disjoint set of edges. We prove that this problem cannot be efficiently approximated to within a factor of \( \Omega {\left( {k/\ln k} \right)} \) unless P = NP. This improves the previous hardness of approximation factor of \( k/2^{{O({\sqrt {\ln k} })}} \) by Trevisan. This result extends to the problem of k-Dimensional-Matching.

Keywords.

Computational complexity hardness of approximation set packing 

Subject classification.

68Q17 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  • Elad Hazan
    • 1
  • Shmuel Safra
    • 2
  • Oded Schwartz
    • 2
  1. 1.Computer Science DepartmentPrinceton UniversityPrincetonU.S.A.
  2. 2.School of Computer ScienceTel Aviv UniversityTel AvivIsrael

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