A new DSATUR-based algorithm for exact vertex coloring

This paper describes a new exact algorithm PASS for the vertex coloring problem based on the well known DSATUR algorithm. At each step DSATUR maximizes saturation degree to select a new candidate vertex to color, breaking ties by maximum degree w.r.t. uncolored vertices. Later Sewell introduced a new tiebreaking strategy, which evaluated available colors for each vertex explicitly. PASS differs from Sewell in that it restricts its application to a particular set of vertices. Overall performance is improved when the new strategy is applied selectively instead of at every step. The paper also reports systematic experiments over 1500 random graphs and a subset of the DIMACS color benchmark

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: Méndez-Díaz, Isabel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentin

Automatic frequency assignment for cellular telephones using constraint satisfaction techniques

We study the problem of automatic frequency assignment for cellular telephone systems. The frequency assignment problem is viewed as the problem to minimize the unsatisfied soft constraints in a constraint satisfaction problem (CSP) over a finite domain of frequencies involving co-channel, adjacent channel, and co-site constraints. The soft constraints are automatically derived from signal strength prediction data. The CSP is solved using a generalized graph coloring algorithm. Graph-theoretical results play a crucial role in making the problem tractable. Performance results from a real-world frequency assignment problem are presented. We develop the generalized graph coloring algorithm by stepwise refinement, starting from DSATUR and augmenting it with local propagation, constraint lifting, intelligent backtracking, redundancy avoidance, and iterative deepening

A Color-Exchange Algorithm for Exact Graph Coloring

DEXCH, a color-exchange exact graph coloring algorithm is presented. On many classes of graphs, DEXCH can, in the mean, find the chromatic number of a graph considerably faster than the DSATUR algorithm. The improvement over DSATUR stems from the ability to reorganize the subset of colored vertices and to detect in certain instances the existence of a complete subgraph of cardinality equal to the number of colors used in the best coloring found so far. The mean improvement over DSATUR is greatest on high edge-density graphs attaining the value of 42% on random graphs of edge-density 0.7 on 64 vertices

Using Differential Evolution for the Graph Coloring

Differential evolution was developed for reliable and versatile function optimization. It has also become interesting for other domains because of its ease to use. In this paper, we posed the question of whether differential evolution can also be used by solving of the combinatorial optimization problems, and in particular, for the graph coloring problem. Therefore, a hybrid self-adaptive differential evolution algorithm for graph coloring was proposed that is comparable with the best heuristics for graph coloring today, i.e. Tabucol of Hertz and de Werra and the hybrid evolutionary algorithm of Galinier and Hao. We have focused on the graph 3-coloring. Therefore, the evolutionary algorithm with method SAW of Eiben et al., which achieved excellent results for this kind of graphs, was also incorporated into this study. The extensive experiments show that the differential evolution could become a competitive tool for the solving of graph coloring problem in the future