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The minimum reload s–t path, trail and walk problems
- Source :
- Discrete Applied Mathematics. (13):1404-1417
- Publisher :
- Elsevier B.V.
-
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 ri,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., ri,j=rj,i) or asymmetric. We also investigate bounded degree graphs and planar graphs. We conclude the paper with the traveling salesman problem with reload costs.
Details
- Language :
- English
- ISSN :
- 0166218X
- Issue :
- 13
- Database :
- OpenAIRE
- Journal :
- Discrete Applied Mathematics
- Accession number :
- edsair.core.ac.uk....967f73a7bfd4962c6e14d9bb806335fb
- Full Text :
- https://doi.org/10.1016/j.dam.2010.03.009