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Shortest Paths with Shortest Detours

Author

Listed:
  • Carolin Torchiani

    (Universität Koblenz-Landau)

  • Jan Ohst

    (Universität Koblenz-Landau)

  • David Willems

    (Universität Koblenz-Landau)

  • Stefan Ruzika

    (Universität Koblenz-Landau)

Abstract

This paper is concerned with a biobjective routing problem, called the shortest path with shortest detour problem, in which the length of a route is minimized as one criterion and, as second, the maximal length of a detour route if the chosen route is blocked is minimized. Furthermore, the relation to robust optimization is pointed out, and we present a new polynomial time algorithm, which computes a minimal complete set of efficient paths for the shortest path with shortest detour problem. Moreover, we show that the number of nondominated points is bounded by the number of arcs in the graph.

Suggested Citation

  • Carolin Torchiani & Jan Ohst & David Willems & Stefan Ruzika, 2017. "Shortest Paths with Shortest Detours," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 858-874, September.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1145-9
    DOI: 10.1007/s10957-017-1145-9
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    References listed on IDEAS

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    1. Zielinski, Pawel, 2004. "The computational complexity of the relative robust shortest path problem with interval data," European Journal of Operational Research, Elsevier, vol. 158(3), pages 570-576, November.
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