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Computational Results with a Cutting Plane Algorithm for Designing Communication Networks with Low-Connectivity Constraints

Author

Listed:
  • Martin Grötschel

    (Konrad-Zuse-Zentrum fur Informationstechnik, Berlin, Germany)

  • Clyde L. Monma

    (Bell Communications Research, Morristown, New Jersey)

  • Mechthild Stoer

    (Konrad-Zuse-Zentrum fur Informationstechnik, Berlin, Germany)

Abstract

We describe a cutting plane approach to the problem of designing survivable fiber optic communication networks. This problem can be formulated as a minimum cost network design problem with certain low-connectivity constraints. Computational results on real-world telephone network design problems demonstrate the effectiveness of our cutting plane method. The facet-inducing inequalities for the convex hull of the solutions to this problem on which our algorithm is based are studied in detail in a companion paper.

Suggested Citation

  • Martin Grötschel & Clyde L. Monma & Mechthild Stoer, 1992. "Computational Results with a Cutting Plane Algorithm for Designing Communication Networks with Low-Connectivity Constraints," Operations Research, INFORMS, vol. 40(2), pages 309-330, April.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:2:p:309-330
    DOI: 10.1287/opre.40.2.309
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    Citations

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    Cited by:

    1. Yogesh K. Agarwal, 2002. "Design of Capacitated Multicommodity Networks with Multiple Facilities," Operations Research, INFORMS, vol. 50(2), pages 333-344, April.
    2. M. Didi Biha & A.R. Mahjoub, 2000. "Steiner k-Edge Connected Subgraph Polyhedra," Journal of Combinatorial Optimization, Springer, vol. 4(1), pages 131-144, March.
    3. Bernard Fortz & Martine Labbé & Francesco Maffioli, 2000. "Solving the Two-Connected Network with Bounded Meshes Problem," Operations Research, INFORMS, vol. 48(6), pages 866-877, December.
    4. Anantaram Balakrishnan & Prakash Mirchandani & Harihara Prasad Natarajan, 2009. "Connectivity Upgrade Models for Survivable Network Design," Operations Research, INFORMS, vol. 57(1), pages 170-186, February.
    5. van de Leensel, R.L.J.M. & Flippo, O.E. & Koster, Arie M.C.A. & Kolen, A.W.J., 1996. "A dynamic programming algorithm for the local access network expansion problem," Research Memorandum 027, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Yogesh Agarwal, 2013. "Design of Survivable Networks Using Three- and Four-Partition Facets," Operations Research, INFORMS, vol. 61(1), pages 199-213, February.
    7. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.

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