Reload cost problems: minimum diameter spanning tree

Wirth, Hans-Christoph; Steffan, Jan

doi:10.1016/s0166-218x(00)00392-9

Cited by 35 publications

(57 citation statements)

References 7 publications

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“…In this work, we are interested in applications involving a new kind of cost, which is associated to the transition through a node via two consecutive arcs of different color. Such costs in [7] are called “reload costs,” and here are considered together with the classical arc costs.…”

Section: Introductionmentioning

confidence: 99%

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On minimum reload cost paths, tours, and flows

2010

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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

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Section: Introductionmentioning

confidence: 99%

“…In this article, we consider several basic network optimization problems under a generalization of the reload cost model introduced in [7], that includes here reload costs as well as regular arc costs. We are given a directed graph G = ( V, A ) with a non‐negative cost w ( a ) for each arc a ∈ A .…”

Section: Introductionmentioning

confidence: 99%

On minimum reload cost paths, tours, and flows

2010

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“…We follow the notation and terminology of [19] where the concept of reload cost was defined. We consider edge colored graphs G, where the colors are taken from a finite set X and χ : E(G) → X is the coloring function.…”

Section: Preliminariesmentioning

confidence: 99%

Parameterized Complexity of the MINCCA Problem on Graphs of Bounded Decomposability

Gözüpek

Özkan

Paul

et al. 2016

Graph-Theoretic Concepts in Computer Science

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Abstract. In an edge-colored graph, the cost incurred at a vertex on a path when two incident edges with different colors are traversed is called reload or changeover cost. The Minimum Changeover Cost Arborescence (MinCCA) problem consists in finding an arborescence with a given root vertex such that the total changeover cost of the internal vertices is minimized. It has been recently proved by Gözüpek et al. [14] that the MinCCA problem is FPT when parameterized by the treewidth and the maximum degree of the input graph. In this article we present the following results for MinCCA:• the problem is W[1]-hard parameterized by the treedepth of the input graph, even on graphs of average degree at most 8. In particular, it is W[1]-hard parameterized by the treewidth of the input graph, which answers the main open problem of [14]; • it is W[1]-hard on multigraphs parameterized by the tree-cutwidth of the input multigraph; • it is FPT parameterized by the star tree-cutwidth of the input graph, which is a slightly restricted version of tree-cutwidth. This result strictly generalizes the FPT result given in [14]; • it remains NP-hard on planar graphs even when restricted to instances with at most 6 colors and 0/1 symmetric costs, or when restricted to instances with at most 8 colors, maximum degree bounded by 4, and 0/1 symmetric costs.

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“…If we define the reload cost of a cycle in G as the sum of the reload costs that arise at its nodes, our objective is to minimize the sum of the reload costs of the cycles in S. We call this problem Minimum Reload Cost Cycle Cover (MinRC3). The concept of reload costs was introduced in the seminal paper [6] where various applications are mentioned. This very natural concept, that models a kind of cost incurred during a transportation/transmission activity, has been, amazingly, considered only recently, so that the list of relevant references is comparatively small [2][3][5] [1].…”

Section: Introductionmentioning

confidence: 99%