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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

The convex recoloring problem: polyhedra, facets and computational experiments

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Author(s):
Campelo, Manoel [1] ; Freire, Alexandre S. [2] ; Lima, Karla R. [3] ; Moura, Phablo F. S. [4] ; Wakabayashi, Yoshiko [4]
Total Authors: 5
Affiliation:
[1] Univ Fed Ceara, Dept Estat & Matemat Aplicada, Fortaleza, Ceara - Brazil
[2] Univ Estadual Campinas, Inst Computacao, Campinas, SP - Brazil
[3] Univ Sao Paulo, Escola Artes Ciencias & Humanidades, Sao Paulo - Brazil
[4] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil
Total Affiliations: 4
Document type: Journal article
Source: MATHEMATICAL PROGRAMMING; v. 156, n. 1-2, p. 303-330, MAR 2016.
Web of Science Citations: 2
Abstract

A coloring of the vertices of a graph is convex if the vertices receiving a common color induce a connected subgraph of . We address the convex recoloring problem: given a graph and a coloring of its vertices, recolor a minimum number of vertices of , so that the resulting coloring is convex. This problem is known to be -hard even when is a path. We show an integer programming formulation for arbitrary graphs, and then specialize it for trees. We study the facial structure of the polytope defined as the convex hull of the integer points satisfying the restrictions of the proposed ILP formulation, present several classes of facet-defining inequalities and the corresponding separation algorithms. We also present a branch-and-cut algorithm that we have implemented for the special case of trees, and show the computational results obtained with a large number of instances. We consider instances which are real phylogenetic trees. The experiments show that this approach can be used to solve instances up to vertices in 2 h, comparing favorably to other approaches that have been proposed in the literature. (AU)

FAPESP's process: 13/19179-0 - Optimization problems on graph partitioning
Grantee:Phablo Fernando Soares Moura
Support type: Scholarships in Brazil - Doctorate
FAPESP's process: 12/17585-9 - Modeling Techniques for Solving Combinatorial Optimization Problems
Grantee:Alexandre da Silva Freire
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
Grantee:Carlos Eduardo Ferreira
Support type: Research Projects - Thematic Grants