Transitive packing

  • Rudolf Müller
  • Andreas S. Schulz
Conference paper

DOI: 10.1007/3-540-61310-2_32

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1084)
Cite this paper as:
Müller R., Schulz A.S. (1996) Transitive packing. In: Cunningham W.H., McCormick S.T., Queyranne M. (eds) Integer Programming and Combinatorial Optimization. IPCO 1996. Lecture Notes in Computer Science, vol 1084. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Rudolf Müller
    • 1
  • Andreas S. Schulz
    • 2
  1. 1.Institut für WirtschaftsinformatikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Fachbereich MathematikTechnische Universität BerlinBerlinGermany

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