The Experts below are selected from a list of 20535 Experts worldwide ranked by ideXlab platform
Daniel Severín - One of the best experts on this subject based on the ideXlab platform.
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LAGOS - A Branch and Price Algorithm for List Coloring Problem
Electronic Notes in Theoretical Computer Science, 2019Co-Authors: Mauro Lucci, Graciela L. Nasini, Daniel SeverínAbstract:Abstract Coloring Problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this work, we present a Branch-and-Price algorithm for the weighted version of the List Coloring Problem, based on the one developed by Mehrotra and Trick (1996) for the Graph Coloring Problem. This version considers non-negative weights associated to each color and it is required to assign a color to each vertex from predetermined lists in such a way the sum of weights of the assigned colors is minimum. Computational experiments show the good performance of our approach, being able to comfortably solve instances whose graphs have up to seventy vertices. These experiences also bring out that the hardness of the instances of the List Coloring Problem does not seem to depend only on quantitative parameters such as the size of the graph, its density, and the size of list of colors, but also on the distribution of colors present in the lists.
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A DSATUR-based algorithm for the Equitable Coloring Problem
Computers & Operations Research, 2015Co-Authors: Isabel Méndez-díaz, Graciela L. Nasini, Daniel SeverínAbstract: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.
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A tabu search heuristic for the Equitable Coloring Problem
Lecture Notes in Computer Science, 2014Co-Authors: Isabel Mendez Diaz, Graciela L. Nasini, Daniel SeverínAbstract: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.
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a tabu search heuristic for the equitable Coloring Problem
International Symposium on Combinatorial Optimization, 2014Co-Authors: Isabel Mendez Diaz, Graciela L. Nasini, Daniel SeverínAbstract: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.
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A polyhedral approach for the equitable Coloring Problem
Discrete Applied Mathematics, 2014Co-Authors: Isabel Méndez-díaz, Graciela L. Nasini, Daniel SeverínAbstract: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.
Cerasela Tanasescu - One of the best experts on this subject based on the ideXlab platform.
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On some applications of the selective graph Coloring Problem
European Journal of Operational Research, 2015Co-Authors: Marc Demange, Tınaz Ekim, Bernard Ries, Cerasela TanasescuAbstract:In this paper we present the Selective Graph Coloring Problem, a generalization of the standard graph Coloring Problem as well as several of its possible applications. Given a graph with a partition of its vertex set into several clusters, we want to select one vertex per cluster such that the chromatic number of the subgraph induced by the selected vertices is minimum. This Problem appeared in the literature under different names for specific models and its complexity has recently been studied for different classes of graphs. Here, we describe different models – some already discussed in previous papers and some new ones – in very different contexts under a unified framework based on this graph Problem. We point out similarities between these models, offering a new approach to solve them, and show some generic situations where the selective graph Coloring Problem may be used. We focus on specific graph classes motivated by each model, and we briefly discuss the complexity of the selective graph Coloring Problem in each one of these graph classes and point out interesting future research directions.
Rongjian Chen - One of the best experts on this subject based on the ideXlab platform.
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mtpso algorithm for solving planar graph Coloring Problem
Expert Systems With Applications, 2011Co-Authors: Shi-jinn Horng, Yuhrau Wang, Muhammad Khurram Khan, Rongjian ChenAbstract:Research highlights? A modified turbulent particle swarm optimization (MTPSO) model is proposed to solve the planar graph. ? MTPSO combines walking one strategy, assessment strategy and turbulent strategy. ? MTPSO can solve the four-colors Problem efficiently and accurately. In this paper, we proposed a modified turbulent particle swarm optimization (named MTPSO) model for solving planar graph Coloring Problem based on particle swarm optimization. The proposed model is consisting of the walking one strategy, assessment strategy and turbulent strategy. The proposed MTPSO model can solve the planar graph Coloring Problem using four-colors more efficiently and accurately. Compared to the results shown in Cui et al. (2008), not only the experimental results of the proposed model can get smaller average iterations but can get higher correction Coloring rate when the number of nodes is greater than 30.
Javier Ramírez - One of the best experts on this subject based on the ideXlab platform.
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The robust Coloring Problem
European Journal of Operational Research, 2003Co-Authors: Javier Yáñez, Javier RamírezAbstract:Abstract Some Problems can be modeled as graph Coloring ones for which the criterion of minimizing the number of used colors is replaced by another criterion maintaining the number of colors as a constraint. Some examples of these Problem types are introduced; it would be the case, for instance, of the Problem of scheduling the courses at a university with a fixed number of time slots––the colors––and with the objective of minimizing the probability to include an edge to the graph with its endpoints equally colored. Based on this example, the new Coloring Problem introduced in this paper will be denoted as the Robust Coloring Problem, RCP for short. It is proved that this optimization Problem is NP-hard and, consequently, only small-size Problems could be solved with exact algorithms based on mathematical programming models; otherwise, for large size Problems, some heuristics are needed in order to obtain appropriate solutions. A genetic algorithm which solves the RCP is outlined.
Graciela L. Nasini - One of the best experts on this subject based on the ideXlab platform.
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LAGOS - A Branch and Price Algorithm for List Coloring Problem
Electronic Notes in Theoretical Computer Science, 2019Co-Authors: Mauro Lucci, Graciela L. Nasini, Daniel SeverínAbstract:Abstract Coloring Problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this work, we present a Branch-and-Price algorithm for the weighted version of the List Coloring Problem, based on the one developed by Mehrotra and Trick (1996) for the Graph Coloring Problem. This version considers non-negative weights associated to each color and it is required to assign a color to each vertex from predetermined lists in such a way the sum of weights of the assigned colors is minimum. Computational experiments show the good performance of our approach, being able to comfortably solve instances whose graphs have up to seventy vertices. These experiences also bring out that the hardness of the instances of the List Coloring Problem does not seem to depend only on quantitative parameters such as the size of the graph, its density, and the size of list of colors, but also on the distribution of colors present in the lists.
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A DSATUR-based algorithm for the Equitable Coloring Problem
Computers & Operations Research, 2015Co-Authors: Isabel Méndez-díaz, Graciela L. Nasini, Daniel SeverínAbstract: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.
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A tabu search heuristic for the Equitable Coloring Problem
Lecture Notes in Computer Science, 2014Co-Authors: Isabel Mendez Diaz, Graciela L. Nasini, Daniel SeverínAbstract: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.
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a tabu search heuristic for the equitable Coloring Problem
International Symposium on Combinatorial Optimization, 2014Co-Authors: Isabel Mendez Diaz, Graciela L. Nasini, Daniel SeverínAbstract: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.
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A polyhedral approach for the equitable Coloring Problem
Discrete Applied Mathematics, 2014Co-Authors: Isabel Méndez-díaz, Graciela L. Nasini, Daniel SeverínAbstract: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.