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BDDs in a Branch and Cut Framework

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Experimental and Efficient Algorithms (WEA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 3503))

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Abstract

Branch & Cut is today’s state-of-the-art method to solve 0/1-integer linear programs. Important for the success of this method is the generation of strong valid inequalities, which tighten the linear programming relaxation of 0/1-IPs and thus allow for early pruning of parts of the search tree.

In this paper we present a novel approach to generate valid inequalities for 0/1-IPs which is based on Binary Decision Diagrams (BDDs). BDDs are a datastructure which represents 0/1-vectors as paths of a certain acyclic graph. They have been successfully applied in computational logic, hardware verification and synthesis.

We implemented our BDD cutting plane generator in a branch-and-cut framework and tested it on several instances of the MAX-ONES problem and randomly generated 0/1-IPs. Our computational results show that we have developed competitive code for these problems, on which state-of-the-art MIP-solvers fall short.

This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS). See www.avacs.org for more information.

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Author information

Authors and Affiliations

  1. Albert-Ludwigs-Universität, Georges-Köhler-Allee 51, 79110, Freiburg im Breisgau, Germany

    Bernd Becker & Ralf Wimmer

  2. Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany

    Markus Behle & Friedrich Eisenbrand

Authors
  1. Bernd Becker
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  2. Markus Behle
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  3. Friedrich Eisenbrand
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  4. Ralf Wimmer
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Editor information

Editors and Affiliations

  1. CTI and Univ. of Patras, Greece

    Sotiris E. Nikoletseas

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© 2005 Springer-Verlag Berlin Heidelberg

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Becker, B., Behle, M., Eisenbrand, F., Wimmer, R. (2005). BDDs in a Branch and Cut Framework. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_39

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  • DOI: https://doi.org/10.1007/11427186_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25920-6

  • Online ISBN: 978-3-540-32078-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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