The Minimum Reload s-t Path/Trail/Walk Problems

Authors:
Laurent Gourvès;Adria Lyra;Carlos Martinhon;Jérôme Monnot
Affiliations:
CNRS, UMR 7024, Paris, France F-75775 and Université de Paris-Dauphine, LAMSADE, Paris, France F-75775;Inst. of Computation, Fluminense Federal University, Niterói, Brazil 24210-240 and CEFET/RJ - Federal Center of Technological Education Celso Suckow da Fonseca, Nova Iguaçu, Brazil 26041 ...;Inst. of Computation, Fluminense Federal University, Niterói, Brazil 24210-240;CNRS, UMR 7024, Paris, France F-75775 and Université de Paris-Dauphine, LAMSADE, Paris, France F-75775
Venue:
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Year:
2009

Citing 3
Cited 3

Reload cost problems: minimum diameter spanning tree

Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Note: The complexity of a minimum reload cost diameter problem

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On minimum changeover cost arborescences

SEA'11 Proceedings of the 10th international conference on Experimental algorithms
Complexity of paths, trails and circuits in arc-colored digraphs

TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Reload cost trees and network design

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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.