GUB Covers and Power-Indexed Formulations for Wireless Network Design

We 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. 292--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. This paper was accepted by Dimitris Bertsimas, optimization.