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 xii∈ N of elements of a compact subset X of Rd whose prefixes Xn=xii=1n, 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 Xn with small optimality gap, i.e., with a small increase in the maximum distance between points of X and the elements of Xn with respect to the optimal solution Xn^star. The paper is a first step in this direction, presenting incremental design algorithms with proven optimality bound for one-parameter families of criteria based on coverings and spacings that both converge to dispersion for large values of their parameter. The examples presented show that the covering-based method outperforms state-of-the-art competitors, including coffee-house, suggesting that it inherits from its guaranteed 50% optimality gap.