On the complexity of approximating k-set packing

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.