Transitive Packing: A Unifying Concept in Combinatorial Optimization
Name
OR-346-00.pdf
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2.82 MB
Format
Adobe PDF
Checksum (MD5)
c06cf1b53e8918de81007cb30777e420
Author(s)
Schulz, Andreas S.
Müller, Rudolf
Date Issued
October 1999
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 346-00
Abstract
This paper attempts to give a better understanding of the facial structure of previously separately investigated polyhedra. It introduces the notion of transitive packing and the transitive packing polytope. Polytopes that turn out to be special cases of the transitive packing polytope are, among others, the node packing polytope, the acyclic subdigraph polytope, the bipartite subgraph polytope, the planar subgraph polytope, the clique partitioning polytope, the partition polytope, the transitive acyclic subdigraph polytope, the interval order polytope, and the relatively transitive subgraph polytope. We give cutting plane proofs for several rich classes of valid inequalities of the transitive packing polytope,in this way introducing generalized cycle, generalized clique, generalized antihole, generalized antiweb, and odd partition inequalities. These classes subsume several known classes of valid inequalities for several of the special cases and give also many new inequalities for several other special cases. For some of the classes we also prove a lower bound for their Gomory-Chvdtal rank. Finally, we relate the concept of transitive packing to generalized (set) packing and covering as well as to balanced and ideal matrices.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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