On the Hardness of Approximating k-Dimensional Matching

We study bounded degree graph problems, mainly the problem of k-Dimensional Matching (k-DM), namely, the problem of finding a maximal matching in a k-partite k-uniform balanced hyper-graph. We prove that k-DM cannot be efficiently approximated to within a factor of O( k ln k ) unless P = NP . This improves the previous factor of k 2O( √ ln ) by Trevisan [Tre01]. For low k values we prove NP-hardness factors of 54 53 − ε, 30 29 − ε and 23 22 − ε for 4-DM, 5-DM and 6-DM respectively. These results extend to the problem of Maximum Independent-Set in (k + 1)-claw-free graphs and the problem of k-Set-Packing. Department of Computer Science, Tel Aviv University, Israel, {eladh,safra,odedsc}@post.tau.ac.il