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