On the Complexity of Solving or Approximating Convex Recoloring Problems

Campêlo, Manoel; Huiban, Cristiana G.; Sampaio, Rudini Menezes; Wakabayashi, Yoshiko

doi:10.1007/978-3-642-38768-5_54

Cited by 6 publications

(2 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Campêlo et al. (2013) showed that the unweighted problem is also

double-struckNP

‐hard in planar graphs with maximum degree 4. The CR also has applications in protein–protein interactions, as presented by Chor et al.…”

Section: Introductionmentioning

confidence: 99%

“…This case is polynomial in trees even in the weighted case where a cost of recoloring is associated with each vertex (Moran and Snir, 2008). Campêlo et al (2013) showed that the unweighted problem is also NP-hard in planar graphs with maximum degree 4. The CR also has applications in protein-protein interactions, as presented by Chor et al (2007).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A heuristic for the convex recoloring problem in graphs

Dantas

Souza

Dias

2020

Int Trans Operational Res

View full text Add to dashboard Cite

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.

show abstract

“…Campêlo et al. (2013) showed that the unweighted problem is also