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Design of Survivable Networks Using Three- and Four-Partition Facets

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  • Yogesh Agarwal

    (Indian Institute of Management, Prabandh Nagar, Lucknow 226 013, India)

Abstract

This paper considers the problem of designing a multicommodity network with single facility type subject to the requirement that under failure of any single edge, the network should permit a feasible flow of all traffic. We study the polyhedral structure of the problem by considering the multigraph obtained by shrinking the nodes, but not the edges, in a k -partition of the original graph. A key theorem is proved according to which a facet of the k -node problem defined on the multigraph resulting from a k -partition is also facet defining for the larger problem under a mild condition. After reviewing the prior work on two-partition inequalities, we develop two classes of three-partition inequalities and a large number of inequality classes based on four-partitions. Proofs of facet-defining status for some of these are provided, while the rest are stated without proof. Computational results show that the addition of three- and four-partition inequalities results in substantial increase in the bound values compared to those possible with two-partition inequalities alone. Problems of 35 nodes and 80 edges with fully dense traffic matrices have been solved optimally within a few minutes of computer time.

Suggested Citation

  • Yogesh Agarwal, 2013. "Design of Survivable Networks Using Three- and Four-Partition Facets," Operations Research, INFORMS, vol. 61(1), pages 199-213, February.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:1:p:199-213
    DOI: 10.1287/opre.1120.1147
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    References listed on IDEAS

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    1. 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.
    2. Geir Dahl & Mechthild Stoer, 1998. "A Cutting Plane Algorithm for Multicommodity Survivable Network Design Problems," INFORMS Journal on Computing, INFORMS, vol. 10(1), pages 1-11, February.
    3. Jeffery L. Kennington & Mark W. Lewis, 2001. "The Path Restoration Version of the Spare Capacity Allocation Problem with Modularity Restrictions: Models, Algorithms, and an Empirical Analysis," INFORMS Journal on Computing, INFORMS, vol. 13(3), pages 181-190, August.
    4. Anantaram Balakrishnan & Thomas L. Magnanti & Joel S. Sokol & Yi Wang, 2002. "Spare-Capacity Assignment For Line Restoration Using a Single-Facility Type," Operations Research, INFORMS, vol. 50(4), pages 617-635, August.
    5. Anantaram Balakrishnan & Thomas Magnanti & Joel Sokol & Yi Wang, 2001. "Telecommunication Link Restoration Planning with Multiple Facility Types," Annals of Operations Research, Springer, vol. 106(1), pages 127-154, September.
    6. Kennington, Jeffery L. & Olinick, Eli V. & Spiride, Gheorghe, 2007. "Basic mathematical programming models for capacity allocation in mesh-based survivable networks," Omega, Elsevier, vol. 35(6), pages 629-644, December.
    7. Sara Mattia, 2012. "Solving survivable two-layer network design problems by metric inequalities," Computational Optimization and Applications, Springer, vol. 51(2), pages 809-834, March.
    8. BIENSTOCK, Daniel & CHOPRA, Sunil & GÜNLÜK, Oktay & TSAI, Chih-Yang, 1998. "Minimum cost capacity installation for multicommodity network flows," LIDAM Reprints CORE 1391, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Thomas L. Magnanti & Prakash Mirchandani & Rita Vachani, 1995. "Modeling and Solving the Two-Facility Capacitated Network Loading Problem," Operations Research, INFORMS, vol. 43(1), pages 142-157, February.
    10. 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.
    11. Clyde L. Monma & David F. Shallcross, 1989. "Methods for Designing Communications Networks with Certain Two-Connected Survivability Constraints," Operations Research, INFORMS, vol. 37(4), pages 531-541, August.
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    Cited by:

    1. Agarwal, Y.K. & Aneja, Y.P. & Jayaswal, Sachin, 2022. "Directed fixed charge multicommodity network design: A cutting plane approach using polar duality," European Journal of Operational Research, Elsevier, vol. 299(1), pages 118-136.
    2. Agarwal, Y.K. & Venkateshan, Prahalad, 2016. "Near optimal design of wavelength routed optical networks," European Journal of Operational Research, Elsevier, vol. 250(3), pages 990-1000.
    3. Yogesh Kumar Agarwal & Prahalad Venkateshan, 2019. "New Valid Inequalities for the Optimal Communication Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 268-284, April.
    4. Kohar, Amit & Jakhar, Suresh Kumar & Agarwal, Yogesh K., 2023. "Strong cutting planes for the capacitated multi-pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 176(C).
    5. Nigam, Ashutosh & Agarwal, Yogesh K., 2014. "Optimal relay node placement in delay constrained wireless sensor network design," European Journal of Operational Research, Elsevier, vol. 233(1), pages 220-233.

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