The paper addresses the problem of defining families of ordered sequences $\{x_i\}_{i\in N}$ 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 $X_n^\star$. 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.

中文翻译：

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基于覆盖和间距的增量空间填充设计：改进低差异序列

该论文解决了定义 $R^d$ 的紧致子集 $X$ 的元素的有序序列族 $\{x_i\}_{i\in N}$ 的问题，其前缀 $X_n=\{x_i\} _{i=1}^{n}$，对于所有订单$n$，根据分散（覆盖半径）标准测量具有良好的空间填充特性。我们的最终目标是定义增量算法，该算法生成具有较小最优性差距的序列 $X_n$，即相对于最优解 $X$ 的点与 $X_n$ 的元素之间的最大距离的小幅增加X_n^\star$。这篇论文是朝着这个方向迈出的第一步，提出了增量设计算法，该算法对基于覆盖和间距的单参数系列标准提出了经过验证的最优性边界，这两者都收敛到其参数的大值的分散。