Optimal deployment of indoor wireless local area networks

We present a two-phase methodology to address the problem of optimally deploying indoor wireless local area networks. In the first phase, we use Helmholtz's equation to simulate electromagnetic fields in a typical environment such as an office floor. The linear system which results from the discretization of this partial differential equation is solved with a state-of-the-art library for sparse linear algebra. In the second phase, we formulate the network deployment problem in the setting of binary linear programming. This formulation employs the simulator output as input parameters, and jointly optimizes the number of access points, their locations, and their emission channels. We prove that this optimization problem is NP-Hard, and use mathematical programming based techniques and heuristics to solve it. We present numerical experiments on medium-sized buildings.