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The Packing Property

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Integer Programming and Combinatorial Optimization (IPCO 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1412))

Abstract

A clutter (V,E) packs if the smallest number of vertices needed to intersect all the edges (i.e. a transversal) is equal to the maxi- mum number of pairwise disjoint edges (i.e. a matching). This terminol- ogy is due to Seymour 1977. A clutter is minimally nonpacking if it does not pack but all its minors pack. A 0,1 matrix is minimally nonpacking if it is the edge-vertex incidence matrix of a minimally nonpacking clutter. Minimally nonpacking matrices can be viewed as the counterpart for the set covering problem of minimally imperfect matrices for the set packing problem. This paper proves several properties of minimally nonpacking clutters and matrices.

This work was supported in part by NSF grants DMI-9424348, DMS-9509581, ONR grant N00014-9710196, a William Larimer Mellon Fellowship, and the Swiss National Research Fund (FNRS).

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Author information

Authors and Affiliations

  1. Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols & Bertrand Guenin

  2. Department of Mathematical Science, Michigan Technical University, Houghton, MI, 49931, USA

    François Margot

Authors
  1. Gérard Cornuéjols
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  2. Bertrand Guenin
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  3. François Margot
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Editor information

Editors and Affiliations

  1. Department of Computational and Applied Mathematics, Rice University, 6020 Annapolis, Houston, TX, 77005, USA

    Robert E. Bixby

  2. PROS Strategic Solutions, 3223 Smith Street, Houston, TX, 77006, USA

    E. Andrew Boyd

  3. Department of Industrial, Engineering, Texas A&M University, 1000 Country Place Dr. Apt. 69, Houston, TX, 77079, USA

    Roger Z. Ríos-Mercado

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© 1998 Springer-Verlag Berlin Heidelberg

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Cornuéjols, G., Guenin, B., Margot, F. (1998). The Packing Property. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds) Integer Programming and Combinatorial Optimization. IPCO 1998. Lecture Notes in Computer Science, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69346-7_1

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  • DOI: https://doi.org/10.1007/3-540-69346-7_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64590-0

  • Online ISBN: 978-3-540-69346-8

  • eBook Packages: Springer Book Archive

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