Column Generation Approach to the Convex Recoloring Problem on a Tree

Chopra, Sunil; Erdem, Ergin; Kim, Eun-Seok; Shim, Sangho

doi:10.1007/978-3-319-66616-7_3

Cited by 2 publications

(6 citation statements)

References 10 publications

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“…Chopra et al. (2016) presented a column generation approach to the problem, solving the same instances when the number of colors is large. Moura (2017) also suggested a column generation approach.…”

Section: Introductionmentioning

confidence: 99%

A heuristic for the convex recoloring problem in graphs

Dantas

Souza

Dias

2020

Int Trans Operational Res

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We consider a coloring as a function that assigns a color to a vertex, regardless of the color of its neighbors. In this sense, a coloring is said to be convex if every set of all same colored vertices induces a connected subgraph. The Convex Recoloring Problem finds the minimum number of recolored vertices needed to turn a coloring convex. This problem is most commonly studied considering trees due to its origins in Computational Biology, but in this paper, we focus on general graphs. We propose a heuristic based on the Greedy Randomized Adaptive Search Procedure to solve the problem. We present computational experiments for our heuristic and compare it to an Integer Linear Programming (ILP) model from the literature. In these experiments, our heuristic recolored at most one vertex more than the ILP model, and it was also able to give better solutions when the ILP model was unable to find the optimal solution within the time limit. We also introduce a set of benchmark instances for the problem.

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Section: Introductionmentioning

confidence: 99%

A heuristic for the convex recoloring problem in graphs

Dantas

Souza

Dias

2020

Int Trans Operational Res

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“…Chopra et al [4] developed a column generation approach to the convex recoloring problem on a tree and successfully solved those problem instances which the integer programming introduced by Chopra et al [5] could not solve. If the number of colors is large, the column generation approach performed extremely fast.…”

Section: Advanced Computingmentioning

confidence: 99%

“…Johnson, Mehrotra and Nemhauser [10] first developed a column generation framework for a clustering problem, and Chopra, Erdem, Kim and Shim [4] adjusted the framework to the convex recoloring problem to recolor nodes of a colored graph at minimum number of color changes such that each color induces a connected subgraph where a pair of nodes colored with a same color Kenneth Gahler is an undergraduate student of Robert Morris University. He performed the small scale of computational experiment using Microsoft Excel in Section 3.1 † Eunseok (Isaac) Kim is a Robert Morris University visiting graduate student from KAIST (Korea Advanced Institute of Technology and Science, South Korea).…”

Section: Introductionmentioning

confidence: 99%

“…In the column generation framework introduced by Chopra et al [4], the subproblem to generate the best contributing column is solved in two steps:…”

Section: Introductionmentioning

confidence: 99%

“…Dantzig's rule selects the column of the best reduced cost and is used in Step 1. Chopra et al [4] used Dantzig's rule in Step 2 as well. Since the columns generated in Step 1 can be enumerated in Step 2, we can apply the steepest edge rule which is suggested by Goldfarb and Reid [9].…”

Section: Introductionmentioning

confidence: 99%

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