On the complexity of approximating k-set packing

Elad Hazan, Shmuel Safra, Oded Schwartz
2006 Computational Complexity  
We study the complexity of bounded packing problems, mainly the problem of k-Set Packing (k-SP), We prove that k-SP cannot be efficiently approximated to within a factor of O( k ln k ) unless P = N P . This improves the previous factor of A similar technique yields NP-hardness factors of 54 53 − ε, 30 29 − ε and 23 22 − ε for 4-SP, 5-SP and 6-SP respectively. These results extend to the problem of k-Dimensional-Matching and the problem of Maximum Independent-Set in (k + 1)-claw-free graphs.
doi:10.1007/s00037-006-0205-6 fatcat:3hemtqt4hrbtzjzwidhlhsqota