Abstract
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) |
|---|---|
| Pages (from-to) | 83-97 |
| Number of pages | 15 |
| Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Volume | 2764 |
| State | Published - Dec 1 2003 |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)