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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abouelaoualim, A., Das, K.C., Faria, L., Manoussakis, Y., Martinhon, C.A., Saad, R.: Paths and trails in edge -colored graphs. Theoretical Computer Science 409(3), 497–510 (2008)
Amaldi, E., Galbiati, G., Maffioli, F.: On minimum reload cost paths, tours and flows. In: Proc. of the Cologne Twente Worshop (CTW 2008) (2008)
Berman, P., Karpinski, M., Scott, A.D.: Approximation Hardness of Short Symmetric Instances of MAX-3SAT. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 49 (2003)
Galbiati, G.: The complexity of a minimum reload cost diameter problem. Discrete Applied Mathematics (article in press, 2008)
Gamvros, I.: Satellite network design, optimization and management PhD thesis, University of Maryland (2006)
Gamvros, I., Gouveia, L., Raghavan, S.: Reload Cost Trees and Network Desig. In: Proc. of the International Network Optimization Conference (INOC 2007) (2007)
Gerards, A.M.H.: Matching: Network Models. North-Holland, Amsterdam (1995)
Wirth, H.C., Steffan, J.: Reload cost problems: minimum diameter spanning tree. Discrete Applied Mathematics 113, 73–85 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gourvès, L., Lyra, A., Martinhon, C., Monnot, J. (2009). The Minimum Reload s-t Path/Trail/Walk Problems. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds) SOFSEM 2009: Theory and Practice of Computer Science. SOFSEM 2009. Lecture Notes in Computer Science, vol 5404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95891-8_55
Download citation
DOI: https://doi.org/10.1007/978-3-540-95891-8_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-95890-1
Online ISBN: 978-3-540-95891-8
eBook Packages: Computer ScienceComputer Science (R0)