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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. Yogesh Agarwal, 2013. "Design of Survivable Networks Using Three- and Four-Partition Facets," Operations Research, INFORMS, vol. 61(1), pages 199-213, February.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).

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