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(0, ±1) ideal matrices

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Integer Programming and Combinatorial Optimization (IPCO 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 920))

Abstract

A (0,1) matrix A is said to be ideal if all the vertices of the polytope Q(A)=x∶Ax ≥ 1,0 ≤x ≤1 are integral. In this paper we consider the extension of the notion of ideality to (0, ±1) matrices. We associate with any (0,±1) matrix A its disjoint completion A + and we show that A is ideal if and only if a suitable (0,1) matrix D(A+) is ideal. Moreover, we prove a Lehman-type characterization of minimally non-ideal (0,±1) matrices that coincide with their disjoint completion.

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References

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Author information

Authors and Affiliations

  1. Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni, 30-00185, Roma, Italy

    Paolo Nobili

  2. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza,”, via Buonarroti, 12-00185, Roma, Italy

    Antonio Sassano

Authors
  1. Paolo Nobili
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  2. Antonio Sassano
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Editor information

Egon Balas Jens Clausen

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© 1995 Springer-Verlag Berlin Heidelberg

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Nobili, P., Sassano, A. (1995). (0, ±1) ideal matrices. In: Balas, E., Clausen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1995. Lecture Notes in Computer Science, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59408-6_63

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  • DOI: https://doi.org/10.1007/3-540-59408-6_63

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59408-6

  • Online ISBN: 978-3-540-49245-0

  • eBook Packages: Springer Book Archive

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