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An exact lexicographic approach for the maximally risk-disjoint/minimal cost path pair problem in telecommunication networks

Author

Listed:
  • Marta Pascoal

    (University of Coimbra, CMUC
    Universidade de Coimbra
    Politecnico di Milano)

  • José Craveirinha

    (Universidade de Coimbra)

  • João Clímaco

    (Universidade de Coimbra)

Abstract

The paper addresses the lexicographically maximal risk-disjoint/minimal cost path pair problem that aims at finding a pair of paths between two given nodes, which is the shortest (in terms of cost) among those that have the fewest risks in common. This problem is of particular importance in telecommunication network design, namely concerning resilient routing models where both a primary and a backup path have to be calculated to minimize the risk of failure of a connection between origin and terminal nodes, in case of failure along the primary path and where bandwidth routing costs should also be minimized. An exact combinatorial algorithm is proposed for solving this problem which combines a path ranking method and a path labelling algorithm. Also an integer linear programming (ILP) formulation is shown for comparison purposes. After a theoretical justification of the algorithm foundations, this is described and tested, together with the ILP procedure, for a set of reference networks in telecommunications, considering randomly generated risks, associated with Shared Risk Link Groups (SRLGs) and arc costs. Both methods were capable of solving the problem instances in relatively short times and, in general, the proposed algorithm was clearly faster than the ILP formulation excepting for the networks with the greatest dimension and connectivity.

Suggested Citation

  • Marta Pascoal & José Craveirinha & João Clímaco, 2022. "An exact lexicographic approach for the maximally risk-disjoint/minimal cost path pair problem in telecommunication networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 405-425, July.
    • Handle: RePEc:spr:topjnl:v:30:y:2022:i:2:d:10.1007_s11750-021-00619-9
    DOI: 10.1007/s11750-021-00619-9
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    References listed on IDEAS

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    1. Jin Y. Yen, 1971. "Finding the K Shortest Loopless Paths in a Network," Management Science, INFORMS, vol. 17(11), pages 712-716, July.
    2. João Clímaco & José Craveirinha & Rita Girão-Silva, 2016. "Multicriteria Analysis in Telecommunication Network Planning and Design: A Survey," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 1167-1233, Springer.
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