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Branch-and-Cut Algorithms for Steiner Tree Problems with Privacy Conflicts

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Computing and Combinatorics (COCOON 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11653))

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Abstract

In this paper we propose two novel variants of the well-known Steiner tree problem in graphs that are motivated by applications in secure strategic telecommunication network design. Both network optimization models ask for a tree of minimal total edge cost that connects a pre-specified set of terminal nodes to a dedicated root node by optionally including intermediate Steiner nodes. Two types of privacy conflicts between pairs of conflicting terminals are considered: (I) The path from the root to a terminal must not include the conflicting terminal, and (II) conflicting terminals have to be on separate branches of the tree. We develop non-compact integer programming formulations and elaborate branch-and-cut algorithms. We incorporate problem specific valid inequalities that are crucial in order to solve these problems, and establish dominance relationships between these cuts and the induced polyhedra. The effectiveness of the cutting planes with respect to the dual bound and the performance of the exact algorithm are assessed on a diverse set of SteinLib-based test instances.

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Notes

  1. 1.

    The test instances can be obtained from the authors upon request.

  2. 2.

    http://people.brunel.ac.uk/~mastjjb/jeb/orlib/steininfo.html.

  3. 3.

    http://steinlib.zib.de.

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Author information

Authors and Affiliations

  1. Department of Industrial & Manufacturing Engineering, California Polytechnic State University, San Luis Obispo, USA

    Alessandro Hill

  2. Institute of Information Systems (IWI), University of Hamburg, Hamburg, Germany

    Stefan Voß

  3. Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi”, University of Bologna, Cesena, Italy

    Roberto Baldacci

Authors
  1. Alessandro Hill
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  2. Stefan Voß
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  3. Roberto Baldacci
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Corresponding author

Correspondence to Alessandro Hill .

Editor information

Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Xidian University, Xi'an, China

    Zhenhua Duan

  3. Xidian University, Xi'an, China

    Cong Tian

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Hill, A., Voß, S., Baldacci, R. (2019). Branch-and-Cut Algorithms for Steiner Tree Problems with Privacy Conflicts. In: Du, DZ., Duan, Z., Tian, C. (eds) Computing and Combinatorics. COCOON 2019. Lecture Notes in Computer Science(), vol 11653. Springer, Cham. https://doi.org/10.1007/978-3-030-26176-4_22

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  • DOI: https://doi.org/10.1007/978-3-030-26176-4_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26175-7

  • Online ISBN: 978-3-030-26176-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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