The convex recoloring problem: polyhedra, facets and computational experiments

Campêlo, Manoel; Freire, André Pimenta; Lima, Karla Roberta; Moura, Phablo F. S.; Wakabayashi, Yoshiko

doi:10.1007/s10107-015-0880-7

Cited by 11 publications

(12 citation statements)

References 13 publications

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“…First, we describe the implementation details of the formulation proposed by Campêlo et al. (2016) (ILP) and present results of our computational tests. The model was solved by IBM's CPLEX (version 12.8).…”

Section: Computational Resultsmentioning

confidence: 99%

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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: Computational Resultsmentioning

confidence: 99%

“…Campêlo et al. (2016) present a proof of correctness to this formulation, as well as a polyhedral study. We implemented the formulation to obtain an exact solution and used it to compare the results with our proposed heuristic.…”

Section: Integer Linear Programming Modelmentioning

confidence: 96%

A heuristic for the convex recoloring problem in graphs

Dantas

Souza

Dias

2020

Int Trans Operational Res

View full text Add to dashboard Cite

show abstract

“…Inequalities (2) require that each vertex receives at most one color, while inequalities (3) require that each color is assigned to at most one connected subgraph. This formulation was introduced in [13] and, independently, in [5] for CR restricted to trees.…”

Section: The Connected Subgraph Polytopementioning

confidence: 99%

“…An integer linear formulation for CR on general graphs was introduced by Campêlo et al in [2]. They presented a detailed polyhedral study and computational experiments on trees.…”

Section: Introductionmentioning

confidence: 99%