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Exact methods for solving the elementary shortest and longest path problems

Author

Listed:
  • Quoc Trung Bui

    (FPT University)

  • Yves Deville

    (Université catholique de Louvain)

  • Quang Dung Pham

    (Hanoi University of Science and Technology)

Abstract

We consider in this paper the problems of finding the elementary shortest and longest paths on a graph containing negative and positive cycles. These problems are NP-hard. We propose exact algorithms based on mixed integer programming for their solution, employing different valid inequalities. Moreover, we propose decomposition techniques which are very efficient for cases with special structure. Experimental results show the efficiency of our algorithms compared with state of the art exact algorithms.

Suggested Citation

  • Quoc Trung Bui & Yves Deville & Quang Dung Pham, 2016. "Exact methods for solving the elementary shortest and longest path problems," Annals of Operations Research, Springer, vol. 244(2), pages 313-348, September.
    • Handle: RePEc:spr:annopr:v:244:y:2016:i:2:d:10.1007_s10479-016-2116-5
    DOI: 10.1007/s10479-016-2116-5
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    References listed on IDEAS

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    1. Moreno, Alfredo & Alem, Douglas & Gendreau, Michel & Munari, Pedro, 2020. "The heterogeneous multicrew scheduling and routing problem in road restoration," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 24-58.

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