Incremental space-filling design based on coverings and spacings: improving upon low discrepancy sequences
The paper addresses the problem of defining families of ordered sequences {x_i} i∈N of elements of a compact subset X of R^d whose prefixes X_n = {x_i} i=1, ..., n, for all orders n, have good space-filling properties as measured by the dispersion (covering radius) criterion. Our ultimate aim is the definition of incremental algorithms that generate sequences X_n with small optimality gap, i.e., with a small increase in the maximum distance between points of X and the elements of X_n with respect to the optimal solution X_n. The paper is a first step in this direction, presenting incremental design algorithms with proven optimality bound with respect to one-parameter families of criteria based on coverings and spacings that both converge to dispersion for large values of their parameter.

Joint work with Luc Pronzato and Maria-Joao Rendas.