几何数据流中的确定性采样和范围计数
Deterministic Sampling and Range Counting in Geometric Data Streams
摘要：
我们提出了内存高效的确定性算法，用于构建几何数据流的ε-网和ε-近似。与概率方法不同，这些确定性样本在其近似因子上提供有保证的界限。我们展示了我们的确定性样本可以用来回答近似的在线冰山几何查询数据流。我们使用这些技术来近似几何数据流的几个强大的统计，包括Tukey深度，单纯深度，回归深度，Thiel-Sen估计，和最小平方中位数。我们的算法只使用多对数的内存量，所需的近似因子是逆多对数。我们还包括一个下界的非冰山几何查询。
英文摘要：
We present memory-efficient deterministic algorithms for constructing epsilon-nets and epsilon-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
