On Minimum Reload Cost Cycle Cover

Galbiati, Giulia; Gualandi, Stefano; Maffioli, Francesco

doi:10.1016/j.endm.2010.05.011

Cited by 17 publications

(37 citation statements)

References 5 publications

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“…The previous results on MinRC3 are as follows:Theorem (Galbiati et al ) . MinRC 3 is strongly NP ‐ hard even if the number of colors is 2, the reload costs are symmetric , and satisfy the triangle inequality . Corollary (Galbiati et al ) . MinRC 3 is not approximable within 1/ ϵ , for any ϵ > 0, even if the number of colors is 2, the reload costs are symmetric , and satisfy the triangle inequality .…”

Section: Preliminariesmentioning

confidence: 99%

“…Galbiati et al introduced the Minimum Reload Cost Cycle Cover (MinRC3) problem, which is to find a set of vertex‐disjoint cycles spanning all vertices with minimum total reload cost. They proved that it is strongly NP‐hard and not approximable within 1/ ϵ for any ϵ > 0 even when the number of colors is 2, the reload costs are symmetric and satisfy the triangle inequality.…”

Section: Introductionmentioning

confidence: 99%

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Minimum reload cost cycle cover in complete graphs

2019

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The reload cost refers to the cost that occurs along a path on an edge‐colored graph when it traverses an internal vertex between two edges of different colors. Galbiati et al. introduced the Minimum Reload Cost Cycle Cover problem, which is to find a set of vertex‐disjoint cycles spanning all vertices with minimum reload cost. They proved that this problem is strongly NP‐hard and not approximable within 1/ϵ for any ϵ > 0 even when the number of colors is 2, the reload costs are symmetric and satisfy the triangle inequality. In this paper, we prove that the minimum reload cost is zero on complete graphs with n vertices and an equitable 2‐edge‐coloring except possibly n = 4 or with a nearly equitable 2‐edge‐coloring except possibly for n ≤ 13. Furthermore, we provide a polynomial‐time algorithm that constructs a monochromatic cycle cover in complete graphs Kn with an equitable 2‐edge‐coloring except possibly for n = 4. This algorithm also finds a monochromatic cycle cover in complete graphs with a nearly equitable 2‐edge‐coloring except for some special cases.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimum reload cost cycle cover in complete graphs

2019

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“…Even within the same technology, switching between different providers, for instance switching between different commercial satellite providers in satellite networks, leads to a switching cost. All applications hitherto mentioned can be modeled using traversal costs where an edge‐colored graph is given as input, and this is the focus of the works in the literature, for example, .…”

Section: Introductionmentioning

confidence: 99%

“…Various problems about the reload cost and changeover cost concept have been studied in the literature: the minimum reload cost diameter spanning tree problem , the minimum reload cost cycle cover problem , the problem of finding a path, trail, or walk of minimum reload cost between two given vertices , the problem of finding a spanning tree that minimizes the sum of reload costs over the paths between all pairs of vertices , the problem of finding a spanning tree that minimizes the reload cost from a given root vertex to all other vertices, and finally the minimum changeover cost arborescence problem, which is to find a spanning tree that minimizes the total changeover cost from a given root vertex to all other vertices .…”

Section: Introductionmentioning

confidence: 99%

Complexity of edge coloring with minimum reload/changeover costs

Gözüpek

Shalom

2018

Networks

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In an edge‐colored graph, a traversal cost occurs along a path when consecutive edges with different colors are traversed. The value of the traversal cost depends only on the colors of the edges. Two related global cost measures, namely the reload cost and the changeover cost with applications in telecommunications, transportation networks, and energy distribution networks have been studied in the literature. Previous work focused on problems with an edge‐colored graph being part of the input. In this paper, we formulate problems that aim to find an edge coloring of a graph minimizing the reload and changeover costs. One pair of problems aims to find a proper edge coloring to minimize the reload/changeover cost of a set of paths. Another pair of problems aim to find a proper edge coloring and a spanning tree to minimize the reload/changeover cost. We present several hardness results and polynomial‐time solvable special cases.

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“…Amaldi et al study the complexity and approximability of the problems of finding optimal paths, tours, and flows under a cost model including reloads and regular costs. In Galbiati et al , the authors consider the minimum reload cost cycle cover problem and prove that it is strongly NP‐hard and not approximable within any

ε > 0

even when the number of colors is 2, reload costs are symmetric and satisfy the triangle inequality. Gourvès et al study the complexity of the minimum reload cost s‐t path, trail, and walk problems with reload costs.…”

Section: Introductionmentioning

confidence: 99%

Efficient Edge‐swapping heuristics for the reload cost spanning tree problem

Raghavan

Şahin

2015

Networks

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The reload cost spanning tree problem (RCSTP) is an NPhard problem, where we are given a set of nonnegative pairwise demands between nodes, each edge is colored and a reload cost is incurred when a color change occurs on the path between a pair of demand nodes. The goal is to find a spanning tree with minimum total reload cost. We propose a tree-nontree edge swap neighborhood for the RCSTP and an efficient way to search this neighborhood using preprocessed information. We then embed this edge swap neighborhood within a local search and a tabu search heuristic. We also discuss an initial solution procedure that is used by the local search and tabu search heuristic in a multistart framework. On a test set of 630 instances (that includes benchmark instances from Gamvros et al.

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On Minimum Reload Cost Cycle Cover

Cited by 17 publications

References 5 publications

Minimum reload cost cycle cover in complete graphs

Minimum reload cost cycle cover in complete graphs

Complexity of edge coloring with minimum reload/changeover costs

Efficient Edge‐swapping heuristics for the reload cost spanning tree problem

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