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A Cutting Plane Algorithm for the Design of survivable Networks

  • Mechthild Stoer
Conference paper
Part of the Operations Research Proceedings book series (ORP, volume 1990)

Abstract

With the high capacity of optical fiber technology it has become possible to design very sparse network topologies, so that some attention has to be given to the design of minimum-cost networks that are survivable against the loss of a single link or node.

Cardwell, Fowler, Lemberg and Monma [CFLM] (see also [CMW]) developed a model for the design of minimum-cost survivable telephone networks; Monma and Shallcross [MS] designed efficient heuristics for this problem, and Grötschel and Monma [GM] looked at several models of survivable network design from the polyhedral point-of-view. Based on this work and further polyhedral investigations the present author together with C. Monma (Bell Communications Research, Morristown, NJ) and M. Grötschel (Augsburg) developed a cutting plane algorithm to solve the problem of survivable network design exactly.

In this paper we present the survivability model and the cutting plane algorithm. More details can be found in [GMS1, GMS2, GMS3].

Keywords

Plane Algorithm Network Design Problem Trivial Inequality Separation Routine Survivable Network Design 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [CFLM]
    : R. H. Cardwell, H. Fowler, H. L. Lemberg and C. L. Monma, “Determining the impact of fiber optic technology on telephone network design”, Bellcore Exchange Magazine, 27–32, March/April 1988.Google Scholar
  2. [CMW]
    : R. H. Cardwell, C. L. Monma and T. H. Wu, “Computer-aided design procedures for survivable fiber optic networks”, IEEE Selected Areas of Communications, 7, 1188–1197, 1989.CrossRefGoogle Scholar
  3. [CPlex]
    : CPlex Optimization, 7710-T Cherry Park, Suite 124, Houston, Texas 77095.Google Scholar
  4. [GH]
    : R. E. Gomory and T. C. Hu, “Multi-Terminal Network Flows,” SIAM Journal on Applied Mathematics 9, 551–570, 1961.Google Scholar
  5. [GM]
    : M. Grötschel and C. L. Monma, “Integer polyhedra associated with certain network design problems with connectivity constraints”, SIAM Journal on Discrete Mathematics, to appear 1990.Google Scholar
  6. [GMS1]
    : M. Grötschel, C. L. Monma and M. Stoer, “Facets for polyhedra arising in the design of communication networks with low-connectivity constraints”, Schwerpunktprogramm der Deutschen Forschungsgemeinschaft, Anwendungsbezogene Optimierung und Steuerung, Report No. 187, 1989.Google Scholar
  7. [GMS2]
    : M. Grötschel, C. L. Monma and M. Stoer, “Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints”, Schwerpunktprogramm der Deutschen Forschungsgemeinschaft, Anwendungsbezogene Optimierung und Steuerung, Report No. 188, 1989.Google Scholar
  8. [GMS3]
    : M. Grötschel, C. L. Monma and M. Stoer, “Polyhedral approaches to network survivability”, Schwerpunktprogramm der Deutschen Forschungsgemeinschaft, Anwendungsbezogene Optimierung und Steuerung, Report No. 189, 1989.Google Scholar
  9. [MS]
    : C. L. Monma and D. F. Shallcross, “Methods for designing communication networks with certain two-connected survivability constraints”, Operations Research, 37, 531–541, 1989.CrossRefGoogle Scholar
  10. [PR]
    : M. W. Padberg and M. R. Rao, “Odd minimum cut sets and b-matchings”, Mathematics of Operations Research, 7, 67–80, 1982.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1992

Authors and Affiliations

  • Mechthild Stoer
    • 1
  1. 1.AugsburgGermany

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