On the complexity of approximating k-set packing

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 ( k ln k ) unless P = NP. This improves the previous hardness of approximation factor of k 2( ln k) by Trevisan [Tre01]. This result extends to the problem of k-Dimensional-Matching.

• Type: Journal
• Year: 2006
• Where: CC
• Authors: Elad Hazan, Shmuel Safra, Oded Schwartz
• Keywords: CC 2006, K-uniform Hypergraph, Maximum Disjoint, Maximum K-set Packing, System Software