461 research outputs found
A DSATUR-based algorithm for the Equitable Coloring Problem
This paper describes a new exact algorithm for the Equitable Coloring Problem, a coloring problem where the sizes of two arbitrary color classes differ in at most one unit. Based on the well known DSatur algorithm for the classic Coloring Problem, a pruning criterion arising from equity constraints is proposed and analyzed. The good performance of the algorithm is shown through computational experiments over random and benchmark instances.Fil: MĂ©ndez-DĂaz, Isabel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de ComputaciĂłn; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, IngenierĂa y Agrimensura; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, IngenierĂa y Agrimensura; Argentin
A polyhedral approach for the Equitable Coloring Problem
In this work we study the polytope associated with a 0,1-integer programming
formulation for the Equitable Coloring Problem. We find several families of
valid inequalities and derive sufficient conditions in order to be
facet-defining inequalities. We also present computational evidence that shows
the efficacy of these inequalities used in a cutting-plane algorithm
Polyhedral results for the Equitable Coloring Problem
In this work we study the polytope associated with a 0/1 integer programming
formulation for the Equitable Coloring Problem. We find several families of
valid inequalities and derive sufficient conditions in order to be
facet-defining inequalities. We also present computational evidence of the
effectiveness of including these inequalities as cuts in a Branch & Cut
algorithm
A tabu search heuristic for the Equitable Coloring Problem
The Equitable Coloring Problem is a variant of the Graph Coloring Problem
where the sizes of two arbitrary color classes differ in at most one unit. This
additional condition, called equity constraints, arises naturally in several
applications. Due to the hardness of the problem, current exact algorithms can
not solve large-sized instances. Such instances must be addressed only via
heuristic methods. In this paper we present a tabu search heuristic for the
Equitable Coloring Problem. This algorithm is an adaptation of the dynamic
TabuCol version of Galinier and Hao. In order to satisfy equity constraints,
new local search criteria are given. Computational experiments are carried out
in order to find the best combination of parameters involved in the dynamic
tenure of the heuristic. Finally, we show the good performance of our heuristic
over known benchmark instances
Mixed integer programming formulations for clustering problems related to structural balance
International audienceIn this work, we study graph clustering problems associated with structural balance. One of these problems is known in computer science literature as the correlation-clustering (CC) problem and another (RCC) can be viewed as its relaxed version. The solution of CC and RCC problems have been previously used in the literature as tools for the evaluation of structural balance in a social network. Our aim is to solve these problems to optimality. We describe integer linear programming formulations for these problems which includes the first mathematical formulation for the RCC problem. We also discuss alternative models for the relaxed structural balance and the solution of clustering problems associated with these new models. Numerical experiments are carried out with each formulation on a set of benchmark instances available in the literature
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