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Improved Formulations for the Ring Spur Assignment Problem

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Book cover Network Optimization (INOC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 6701))

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Abstract

We present two complete integer programming formulations for the ring spur assignment problem. This problem arises in the design of next generation telecommunications networks. We analyse and compare the formulations in terms of compactness, the resulting LP bound and results from a branch and cut implementation. We present our conclusions with computational results.

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References

  1. Bayvel, P.: Future high-capacity optical telecommunication networks. Philosophical Transactions - A - Mathematical Physical and Engineering Sciences 358(1765), 303 (2000)

    Article  MATH  Google Scholar 

  2. Campêlo, M., Campos, V.A., Corrêa, R.C.: On the asymmetric representatives formulation for the vertex coloring problem. Discrete Applied Mathematics 156(7), 1097–1111 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Carroll, P., McGarraghy, S.: An algorithm for the ring spur assignment problem. In: Papova, N., O’hEigheartaigh, M. (eds.) Proceedings of the International Eugene Lawler PhD Summer School 2009 held at WIT, Ireland, June 6-10, pp. 180–197. Scientific Computing, WIT (June 2009)

    Google Scholar 

  4. Carroll, P., McGarraghy, S.: Investigation of the ring spur assignment problem. In: Bigi, G., Frangioni, A., Scutellà, M. (eds.) Proceedings of the 4th International Network Optimization Conference (INOC 2009), April 26-29, pp. MB1–3. INOC, Pisa (2009)

    Google Scholar 

  5. Cosares, S., Deutsch, D.N., Saniee, I., Wasem, O.J.: Sonet toolkit: A decision support system for designing robust and cost-effective fiber-optic networks. Interfaces 25(1), 20–40 (1995)

    Article  Google Scholar 

  6. Fortz, B., Labbé, M.: Two-connected networks with rings of bounded cardinality. Computational Optimization and Applications 27(2), 123–148 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fortz, B., Mahjoub, A.R., McCormick, S.T., Pesneau, P.: Two-edge connected subgraphs with bounded rings: Polyhedral results and Branch-and-Cut. Mathematical Programming 105(1), 85–111 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fortz, B., Soriano, P., Wynants, C.: A tabu search algorithm for self-healing ring network design. European Journal of Operational Research 151(2), 280–295 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Goldschmidt, O., Laugier, A., Olinick, E.V.: SONET/SDH ring assignment with capacity constraints. Discrete Applied Mathematics 129(1), 99–128 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Grover, W., Doucette, J., Clouqueur, M., Leung, D., Stamatelakis, D.: New options and insights for survivable transport networks. IEEE Communications Magazine 40(1), 34–41 (2002)

    Article  Google Scholar 

  11. Grover, W.: Mesh Based Sruvivable Networks, Options and Strategies for Optical, MPLS, Sonet and ATM Networking. Prentice Hall, Englewood Cliffs (2003)

    Google Scholar 

  12. Kerivin, H., Mahjoub, A.: Design of survivable networks. Networks 46(1), 1–21 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Labbé, M., Laporte, G., Martin, I., Salazar-Gonzalez, J.: The Ring Star Problem: Polyhedral analysis and exact algorithm. Networks 43(3), 177–189 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Macambira, E., Maculan, N., de Souza, C.: A column generation approach for SONET ring assignment. Networks 47(3), 157–171 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Orlowski, S., Pióro, M., Tomaszewski, A., Wessäly, R.: SNDlib 1.0–Survivable Network Design Library. Networks 55(3), 276–286 (2010), http://www3.interscience.wiley.com/journal/122653325/abstract

    Google Scholar 

  16. Papadimitriou, G., Obaidat, M., Pomportsis, A.: Advances in Optical Networking. Int. J. Commun. Sys. 15, 101–113 (2001)

    Article  MATH  Google Scholar 

  17. Stoer, M., Wagner, F.: A simple min-cut algorithm. Journal of the ACM 44(4), 585–591 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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Carroll, P., Fortz, B., Labbé, M., McGarraghy, S. (2011). Improved Formulations for the Ring Spur Assignment Problem. In: Pahl, J., Reiners, T., Voß, S. (eds) Network Optimization. INOC 2011. Lecture Notes in Computer Science, vol 6701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21527-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-21527-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21526-1

  • Online ISBN: 978-3-642-21527-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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