, Volume 15, Issue 1, pp 20-39

On the complexity of approximating k-set packing

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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 \( \Omega {\left( {k/\ln k} \right)} \) 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.