不确定数据的范围计数核心集
Range Counting Coresets for Uncertain Data
摘要：
我们研究了不确定数据上各种类型的范围计数查询的核心集。在我们的模型中，每个不确定点都有一个描述其位置的概率密度，有时定义为k个不同的位置。我们的目标是构建一个子集的不确定点，包括其位置的不确定性，范围计数查询可以回答只是检查这个子集。我们研究三种不同类型的查询。RE查询返回查询范围内的预期点数。RC查询返回范围内的点的数量，概率至少为阈值。RQ查询返回小于某个阈值分数的点在范围内的概率。在RC和RQ coresets中，阈值都是作为查询的一部分提供的。对于每一种类型的查询，我们提供的coreset结构与近似大小的权衡。我们表明，随机抽样可以用来构建每一种类型的核心集，我们还提供了显着改进的界限，使用基于差异的方法轴对齐的范围查询。
英文摘要：
We study coresets for various types of range counting queries on uncertain data. In our model each uncertain point has a probability density describing its location, sometimes defined as k distinct locations. Our goal is to construct a subset of the uncertain points, including their locational uncertainty, so that range counting queries can be answered by just examining this subset. We study three distinct types of queries. RE queries return the expected number of points in a query range. RC queries return the number of points in the range with probability at least a threshold. RQ queries returns the probability that fewer than some threshold fraction of the points are in the range. In both RC and RQ coresets the threshold is provided as part of the query. And for each type of query we provide coreset constructions with approximation-size tradeoffs. We show that random sampling can be used to construct each type of coreset, and we also provide significantly improved bounds using discrepancy-based approaches on axis-aligned range queries.
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