: In this paper, a generic tabu search is presented for three coloring problems: graph coloring, T-colorings and set T-colorings. This algorithm integrates important features such as greedy initialization, solution re-generation, dynamic tabu tenure, incremental evaluation of solutions and constraint handling techniques. Empirical comparisons show that this algorithm approaches the best coloring algorithms and outperforms some hybrid algorithms on a wide range of benchmarks. Experiments on large random instances of T-colorings and set T-colorings show encouraging results. 3.1 INTRODUCTION The graph coloring problem is one of the most studied NP-hard problems and can be defined informally as follows. Given an undirected graph, one wishes to color the nodes of the graph with a minimal number of colors in such a way that two colors assigned to two adjacent nodes must be di#erent, i.e., have a minimal distance greater than zero. Graph coloring has many practical applications such as timet...

The problem considered in this paper consists in defining an assignment of frequencies to radio links, to be established between base stations and mobile transmitters, which minimizes the global interference over a given region. This problem is NP-hard and few results have been reported on techniques for solving it to optimality. We have applied to this version of the frequency assignment problem an ANTS metaheuristic, that is an approach following the ACO optimization paradigm. Computational results, obtained on a number of standard problem instances, testify the effectiveness of the proposed approach. 1. Introduction The introduction of mobile communication, such as portable phones, has a tremendous impact on everyday life. Mobility raises a number of research questions: for many of them discrete models and algorithms are required in order to solve the underlying mathematical problem. The Ant Colony Optimization paradigm (ACO) [Dorigo and Di Caro, 1999], [Maniezzo and Carbo...

The problems of assigning frequencies to transmitters can be naturally modelled by generalizations of graph coloring problems. We start with a randomized graph coloring algorithm of Petford and Welsh and propose a randomized algorithm for minimizing the number of constraints violated when a set of frequencies available is xed. Experiments on instances of various types relevant to mobile communication networks are reported.

We study a problem coming from the design of wireless cellular radiocommunication network. Frequency planning constraints are modelled in terms of graph theory. For each planning function f let us call sp(f) - or the span of the frequency planning f - the difference between the largest and the smallest frequency used. Let the Order of the graph be Or(G) = sp(G)+1 and the maximal local order of the graph the maximum order of a clique of G, i.e. M lo(G) = max X clique of G sp(X). We show: M lo(G) sp(G) 8d Mlo(G) 6 e. Keywords: Graph coloring, Frequency planning R'esum'e Ce rapport explore un probl`eme issue de l'allocation de fr'equence dans les r'eseaux de radiocommunication cellulaire. Le probl`eme de planification est d'ecrit `a l'aide de la th'eorie des graphes. Pour une fonction donn'ee f de plannification, on appelle le span de f - ou sp(f) - la diff'erence entre la plus grande fr'equence employ'ee et la plus petite. Nous d'efinissons aussi l'ordre du graphe c...

this paper the frequency planning constraints are modeled in terms of graph theory.