A Generalization of Odd Set Inequalities for the Set Packing Problem
The set packing problem, sometimes also called the stable set problem, is a well-known NP-hard problem in combinatorial optimization with a wide range of applications and an interesting polyhedral structure, that has been the subject of intensive study. We contribute to this field by showing how, employing cliques, odd set inequalities for the matching problem can be generalized to valid inequalities for the set packing polytope with a clear combinatorial meaning.
- 1.Borndörfer, R. (1998). Aspects of set packing, partitioning, and covering, PhD thesis, TU Berlin.Google Scholar
- 2.Borndörfer, R., Heismann, O. (2012). The hypergraph assignment problem. Technical Report 12–14, ZIB.Google Scholar
- 3.Edmonds, J. (1965). Maximum matching and a polyhedron with 0, 1-vertices. Journal of Research of the National Bureau of Standards, 69, 125–130.Google Scholar
- 4.Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness (Series of books in the mathematical sciences). San Francisco: W.H. Freeman.Google Scholar
- 5.Pêcher, A., & Wagler, A. (2006). Generalized clique family inequalities for claw-free graphs. Electronic Notes in Discrete Mathematics, 25, 117–121.Google Scholar