Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, wireless LANs, and military operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modeling ideas for each of the features of the problem, such as the handling of interference among radio signals, the availability of frequencies, and the optimization criterion.This survey gives an overview of the models and methods that the literature provides on the topic. We present a broad description of the practical settings in which frequency assignment is applied. We also present a classification of the different models and formulations described in the literature, such that the common features of the models are emphasized. The solution methods are divided in two parts. Optimization and lower bounding techniques on the one hand, and heuristic search techniques on the other hand. The literature is classified according to the used methods. Again, we emphasize the common features, used in the different papers. The quality of the solution methods is compared, whenever possible, on publicly available benchmark instances. This is an updated version of a paper that appeared in 4OR 1, 261-317, 2003.

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Given a directed graph G(V,A), the p-Median problem consists of determining p nodes (the median nodes) minimizing the total distance from the other nodes of the graph. We present a Branch-and-Cut-and-Price algorithm yielding provably good solutions for instances with vertical bar V vertical bar <= 3795. Key ingredients of the algorithm are a delayed column-and-row generation technique, exploiting the special structure of the formulation, to solve the LP-relaxation, and cutting planes to strengthen the formulation and limit the size of the enumeration tree

W e propose a pure 0-1 formulation for the wireless network design problem, i.e., the problem of configuring a set of transmitters to provide service coverage to a set of receivers. In contrast with classical mixed-integer formulations, where power emissions are represented by continuous variables, we consider only a finite set of power values. This has two major advantages: it better fits the usual practice and eliminates the sources of numerical problems that heavily affect continuous models. A crucial ingredient of our approach is an effective basic formulation for the single knapsack problem representing the coverage condition of a receiver. This formulation is based on the generalized upper bound (GUB) cover inequalities introduced by Wolsey [Wolsey L (1990) Valid inequalities for 0-1 knapsacks and mips with generalised upper bound constraints. Discrete Appl. Math. 29(2-3):251-261]; and its core is an extension of the exact formulation of the GUB knapsack polytope with two GUB constraints. This special case corresponds to the very common practical situation where only one major interferer is present. We assess the effectiveness of our formulation by comprehensive computational results over realistic instances of two typical technologies, namely, WiMAX and DVB-T

Given a simple graph G(V, E) and a set of traffic demands between the nodes of G, the Network Loading Problem consists of installing minimum cost integer capacities on the edges of G allowing routing of traffic demands. In this paper we study the Capacity Formulation of the Network Loading Problem, introducing the new class of Tight Metric Inequalities, that completely characterize the convex hull of the integer feasible solutions of the problem. We present separation algorithms for Tight Metric Inequalities and a cutting plane algorithm, reporting on computational experience. (c) 2006 Elsevier B.V. All rights reserved

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symptomatic plaques were associated with hypoechoic and predominant homogeneous echo-pattern whereas the asymptomatic ones were associated with hyperechoic and less predominant homogeneous pattern.

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