On minimum reload cost paths, tours, and flows

Authors:
Edoardo Amaldi;Giulia Galbiati;Francesco Maffioli
Affiliations:
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy;Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Venue:
Networks
Year:
2011

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Abstract

The concept of reload cost, that is of a cost incurred when two consecutive arcs along a path are of different types, naturally arises in a variety of applications related to transportation, telecommunication, and energy networks. Previous work on reload costs is devoted to the problem of finding a spanning tree of minimum reload cost diameter (with no arc costs) or of minimum reload cost. In this article, we investigate the complexity and approximability of the problems of finding optimum paths, tours, and flows under a general cost model including reload costs as well as regular arc costs. Some of these problems, such as shortest paths and minimum cost flows, turn out to be polynomially solvable while others, such as minimum shortest path tree and minimum unsplittable multicommodity flows, are NP-hard to approximate within any polynomial-time computable function. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(3), 254–260 2011 © 2011 Wiley Periodicals, Inc.