We study the complexity of bounded variants of 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 k) 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 k-Set-Packing and the problem of Maximum Independent-Set in (k + 1)-claw-free graphs.
|Original language||English (US)|
|Number of pages||15|
|Journal||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|State||Published - Dec 1 2003|
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)