Transitive packing
 Rudolf Müller,
 Andreas S. Schulz
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Abstract
This paper is intended to give a concise understanding of the facial structure of previously separately investigated polyhedra. We introduce the notion of transitive packing and the transitive packing polytope and give cutting plane proofs for huge classes of valid inequalities of this polytope. We introduce generalized cycle, generalized clique, generalized antihole, generalized antiweb, generalized web, and odd partition inequalities. These classes subsume several known classes of valid inequalities for several of the special cases but also give many new inequalities for several others. For some of the classes we also prove a nontrivial lower bound for their Chvátal rank. Finally, we relate the concept of transitive packing to generalized (set) packing and covering as well as to balanced and ideal matrices.
 Title
 Transitive packing
 Book Title
 Integer Programming and Combinatorial Optimization
 Book Subtitle
 5th International IPCO Conference Vancouver, British Columbia, Canada, June 3–5, 1996 Proceedings
 Pages
 pp 430444
 Copyright
 1996
 DOI
 10.1007/3540613102_32
 Print ISBN
 9783540613107
 Online ISBN
 9783540684534
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1084
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Rudolf Müller ^{(1)}
 Andreas S. Schulz ^{(2)}
 Author Affiliations

 1. Institut für Wirtschaftsinformatik, HumboldtUniversität zu Berlin, D10178, Berlin, Germany
 2. Fachbereich Mathematik, Technische Universität Berlin, D10623, Berlin, Germany
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