This paper provides a detailed discussion of wireless resource and channel allocation schemes. We provide a survey of a large number of published papers in the area of fixed, dynamic and hybrid allocation schemes and compare their trade-offs in terms of complexity and performance. We also investigate these channel allocation schemes based on other factors such as distributed/centralized control and adaptability to traffic conditions. Moreover, we provide a detailed discussion on reuse partitioning schemes, effect of hand-offs and prioritization schemes. Finally, we discuss other important issues in resource allocation such as overlay cells, frequency planning, and power control. 1 Introduction Technological advances and rapid development of handheld wireless terminals have facilitated the rapid growth of wireless communications and mobile computing. Taking ergonomics and economics factors into account, and considering the new trends in the telecommunications industry to provide ubiqui...

A recent and very promising approach for combinatorial optimization is to embed local search into the framework of evolutionary algorithms. In this paper, we present such hybrid algorithms for the graph coloring problem. These algorithms combine a new class of highly specialized crossover operators and a well-known tabu search algorithm. Experiments of such a hybrid algorithm are carried out on large DIMACS Challenge benchmark graphs. Results prove very competitive with and even better than those of state-of-the-art algorithms. Analysis of the behavior of the algorithm sheds light on ways to further improvement. Keywords: Graph coloring, solution recombination, tabu search, combinatorial optimization. 1 Introduction A recent and very promising approach for combinatorial optimization is to embed local search into the framework of population based evolutionary algorithms, leading to hybrid evolutionary algorithms (HEA). Such an algorithm is essentially based on two key elements: an eff...

We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph). We use a column generation method for implicit optimization of the linear program at each node of the branch-and-bound tree. This approach, while requiring the solution of a difficult subproblem as well as needing sophisticated branching rules, solves small to moderate size problems quickly. We have also implemented an exact graph coloring algorithm based on DSATUR for comparison. Implementation details and computational experience are presented. 1 INTRODUCTION The graph coloring problem is one of the most useful models in graph theory. This problem has been used to solve problems in school timetabling [10], computer register allocation [7, 8], electronic bandwidth allocation [11], and many other areas. These applications suggest that effective algorithms for solving the graph coloring problem would be of great importance. D...

Graph coloring has been employed since the 1980s to efficiently compute sparse Jacobian and Hessian matrices using either finite differences or automatic differentiation. Several coloring problems occur in this context, depending on whether the matrix is a Jacobian or a Hessian, and on the specifics of the computational techniques employed. We consider eight variant vertexcoloring problems here. This article begins with a gentle introduction to the problem of computing a sparse Jacobian, followed by an overview of the historical development of the research area. Then we present a unifying framework for the graph models of the variant matrixestimation problems. The framework is based upon the viewpoint that a partition of a matrixinto structurally orthogonal groups of columns corresponds to distance-2 coloring an appropriate graph representation. The unified framework helps integrate earlier work and leads to fresh insights; enables the design of more efficient algorithms for many problems; leads to new algorithms for others; and eases the task of building graph models for new problems. We report computational results on two of the coloring problems to support our claims. Most of the methods for these problems treat a column or a row of a matrixas an atomic entity, and partition the columns or rows (or both). A brief review of methods that do not fit these criteria is provided. We also discuss results in discrete mathematics and theoretical computer science that intersect with the topics considered here.

The ever growing number of wireless communications systems deployed around the globe have made the optimal assignment of a limited radio frequency spectrum a problem of primary importance. At issue are planning models for permanent spectrum allocation, licensing, regulation, and network design. Further at issue are on-line algorithms for dynamically assigning frequencies to users within an established network. Applications include aeronautical mobile, land mobile, maritime mobile, broadcast, land fixed (pointto -point), and satellite systems. This paper surveys research conducted by theoreticians, engineers, and computer scientists regarding the frequency assignment problem (FAP) in all of its guises. The paper begins by defining some of the more common types of FAPs. It continues with a discussion on measures of optimality relating to the use of spectrum, models of interference, and mathematical representations of the many FAPs, both in graph theoretic terms, and as mathematical pro...

: 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...

this paper, we introduce two such metrics: the worst-case number of channels required to accommodate all possible configurations of N calls in a cell cluster, and the set of cell states that can be accommodated with M channels. We first measure two extreme policies, fixed channel allocation and maximum packing, under these metrics. We then prove a new lower bound, under the first metric, on any channel assignment policy. Next, we introduce three intermediate channel assignment policies, based on commonly used ideas of channel ordering, hybrid assignment, and partitioning. Finally, these policies are used to demonstrate the tradeoff between the performance and the complexity of a channel allocation policy. 1 Introduction

Finding a good graph coloring quickly is often a crucial phase in the development of efficient, parallel algorithms for many scientific and engineering applications. In this paper we consider the problem of solving the graph coloring problem itself in parallel. We present a simple and fast parallel graph coloring heuristic that is well suited for shared memory programming and yields an almost linear speedup on the PRAM model. We also present a second heuristic that improves on the number of colors used. The heuristics have been implemented using OpenMP. Experiments conducted on an SGI Cray Origin 2000 super computer using very large graphs from finite element methods and eigenvalue computations validate the theoretical run-time analysis.

Cellular data and communication networks are usually modeled as graphs with each node representing a base station in a cell in the network, and edges representing geographical adjacency of cells. The problem of channel assignment in such networks can be seen as a graph multicoloring problem. We survey the models, algorithms, and lower bounds for this problem.

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...