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A Class of Label-Correcting Methods for the K Shortest Paths Problem

Author

Listed:
  • Francesca Guerriero

    (Università degli Studi della Calabria, Rende, Italy)

  • Roberto Musmanno

    (Università degli Studi di Lecce, Lecce, Italy, roberto)

  • Valerio Lacagnina

    (Università degli Studi di Palermo, Palermo, Italy)

  • Antonio Pecorella

    (Università degli Studi di Palermo, Palermo, Italy)

Abstract

In this paper we deal with the problem of finding the first K shortest paths from a single origin node to all other nodes of a directed graph. In particular, we define the necessary and sufficient conditions for a set of distance label vectors, on the basis of which we propose a class of methods which can be viewed as an extension of the generic label-correcting method for solving the classical single-origin all-destinations shortest path problem. The data structure used is characterized by a set of K lists of candidate nodes, and the proposed methods differ in the strategy used to select the node to be extracted at each iteration. The computational results show that: 1. some label-correcting methods are generally much faster than the double sweep method of Shier (1979); 2. the most efficient node selection strategies, used for solving the classical single-origin all-destinations shortest path problem, have proved to be effective also in the case of the K shortest paths.

Suggested Citation

  • Francesca Guerriero & Roberto Musmanno & Valerio Lacagnina & Antonio Pecorella, 2001. "A Class of Label-Correcting Methods for the K Shortest Paths Problem," Operations Research, INFORMS, vol. 49(3), pages 423-429, June.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:3:p:423-429
    DOI: 10.1287/opre.49.3.423.11217
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    References listed on IDEAS

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    1. Stuart E. Dreyfus, 1969. "An Appraisal of Some Shortest-Path Algorithms," Operations Research, INFORMS, vol. 17(3), pages 395-412, June.
    2. Azevedo, JoseAugusto & Santos Costa, Maria Emilia O. & Silvestre Madeira, Joaquim Joao E. R. & Vieira Martins, Ernesto Q., 1993. "An algorithm for the ranking of shortest paths," European Journal of Operational Research, Elsevier, vol. 69(1), pages 97-106, August.
    3. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
    4. Jin Y. Yen, 1971. "Finding the K Shortest Loopless Paths in a Network," Management Science, INFORMS, vol. 17(11), pages 712-716, July.
    5. Eugene L. Lawler, 1972. "A Procedure for Computing the K Best Solutions to Discrete Optimization Problems and Its Application to the Shortest Path Problem," Management Science, INFORMS, vol. 18(7), pages 401-405, March.
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    Cited by:

    1. Festa, P. & Guerriero, F. & Laganà, D. & Musmanno, R., 2013. "Solving the shortest path tour problem," European Journal of Operational Research, Elsevier, vol. 230(3), pages 464-474.
    2. Luigi Di Puglia Pugliese & Francesca Guerriero, 2016. "On the shortest path problem with negative cost cycles," Computational Optimization and Applications, Springer, vol. 63(2), pages 559-583, March.

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