Characterization and generation of α-dense curves

If a curve ranges through a cube H = Πni=1[ai, bi] so that, for every point x H, there is at least a point in the curve at a distance not greater than a positive number α, the curve is called α-dense in H. It is very important in the construction of such curves to find algorithms of approximation for global optimization and, in fact, there are several methods to do it, e.g., [1–3]. In this paper, we give a characterization of such curves in terms of γ-stochastically independent functions, as well as a constructive method to generate them by means of only one function called γ-uniformly distributed. Finally, in the above class, i.e., in the set of the γ-uniformly distributed functions, we will choose one of them, will construct the corresponding curve, and will compute its theoretic calculation time.