On the complexity of approximating k-set packing

Authors:
Elad Hazan;Shmuel Safra;Oded Schwartz
Affiliations:
Computer Science Department, Princeton University, Princeton, NJ;School of Computer Science, Tel Aviv University, Tel Aviv, Israel;School of Computer Science, Tel Aviv University, Tel Aviv, Israel
Venue:
Computational Complexity
Year:
2006

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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 Ω(k/ln k) unless P = NP. This improves the previous hardness of approximation factor of k/2O(√lnk) by Trevisan. This result extends to the problem of k-Dimensional-Matching.