Chapter

Integer Programming and Combinatorial Optimization

Volume 1084 of the series Lecture Notes in Computer Science pp 430-444

Date:

Transitive packing

  • Rudolf MüllerAffiliated withInstitut für Wirtschaftsinformatik, Humboldt-Universität zu Berlin
  • , Andreas S. SchulzAffiliated withFachbereich Mathematik, Technische Universität Berlin

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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.