Approximation of a direction of Nd in bounded co - ordinatesJean -

In this paper, we address the following problem: a direction in R d is given by a vector with large integral coordinates and we have to nd a vector with bounded integral coordinates which realizes a good approximation of this direction. We present a short algorithm that eeciently computes an optimal approximation with respect to the distance to the direction. We then compare experimental results with that of a straightforward rounding algorithm with respect to the distance to the direction and to the angle with it. 1. Motivations The Global Standard for Mobility (GSM) (see, e.g., 6], 4], 5]) yields a number of speciic algorithmic problems that can be solved using combinatorics, discrete mathematics or discrete modeling. The frequency assignment problem is the most classical of these problems. Given a GSM network, one wants to assign the frequencies of the Base Transceiver Stations (BTS) in such a way that (adjacent and cochannel) interferences are minimized. Several methods using graph theoretical approaches, simulated annealing or tabu research were proposed in the literature to solve this last problem (see, e.g., 3], 2]). There are lots of other discrete problems that occurs in the context of GSM. To give another interesting example, one can consider the problem of minimizing the cost of the interconnections between the networks of two diierent GSM providers. Such a