The minimum reload s-t path, trail and walk problems

  • Authors:

  • Laurent Gourvès;Adria Lyra;Carlos Martinhon;Jérôme Monnot

  • Affiliations:

  • CNRS, FRE 3234, F-75775 Paris, France and Université de Paris-Dauphine, LAMSADE, F-75775 Paris, France;Fluminense Federal University, Inst. of Computation, 24210-240, Niterói, RJ, Brazil and CEFET/RJ - Federal Center of Technological Education Celso Suckow da Fonseca, Adrianópolis Street, ...;Fluminense Federal University, Inst. of Computation, 24210-240, Niterói, RJ, Brazil;CNRS, FRE 3234, F-75775 Paris, France and Université de Paris-Dauphine, LAMSADE, F-75775 Paris, France

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2010

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Abstract

This paper deals with problems on non-oriented edge-colored graphs. The aim is to find a route between two given vertices s and t. This route can be a walk, a trail or a path. Each time a vertex is crossed by a walk there is an associated non-negative reload cost r"i","j, where i and j denote, respectively, the colors of successive edges in this walk. The goal is to find a route whose total reload cost is minimum. Polynomial algorithms and proofs of NP-hardness are given for particular cases: when the triangle inequality is satisfied or not, when reload costs are symmetric (i.e., r"i","j=r"j","i) or asymmetric. We also investigate bounded degree graphs and planar graphs. We conclude the paper with the traveling salesman problem with reload costs.