computational complexity

, Volume 15, Issue 1, pp 20–39

On the complexity of approximating k-set packing

  • Elad Hazan
  • Shmuel Safra
  • Oded Schwartz
Original Paper

DOI: 10.1007/s00037-006-0205-6

Cite this article as:
Hazan, E., Safra, S. & Schwartz, O. comput. complex. (2006) 15: 20. doi:10.1007/s00037-006-0205-6

Abstract.

Given a k-uniform hypergraph, the Maximumk -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 complexityhardness of approximationset packing

Subject classification.

68Q17

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