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Exact methods for solving the elementary shortest and longest path problems

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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.

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Notes

  1. This arc-flow formulation is presented in Sect. 2.1.

  2. We would like to thank Michael Drexl, the author of Drexl and Irnich (2012), for this information.

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Acknowledgments

We thanks the anonymous reviewers for their helpful and constructive comments. This research was partially sponsored by Vietnamese National Foundation for Science and Technology Development (project FWO.102.2013.04), and by the UCLouvain Action de Recherche Concertee ICTM22C1.

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Authors and Affiliations

  1. FPT Technology Research Institute, FPT University, 8 Ton That Thuyet, Tu Liem, Hanoi, Vietnam

    Quoc Trung Bui

  2. ICTEAM Institute, Université catholique de Louvain, 1348, Louvain-la-Neuve, Belgium

    Yves Deville

  3. School of Information and Communication Technology, Hanoi University of Science and Technology, Hanoi, Vietnam

    Quang Dung Pham

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  1. Quoc Trung Bui
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Correspondence to Yves Deville.

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Bui, Q.T., Deville, Y. & Pham, Q.D. Exact methods for solving the elementary shortest and longest path problems. Ann Oper Res 244, 313–348 (2016). https://doi.org/10.1007/s10479-016-2116-5

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