The range closest-pair (RCP) problem, as a range-search version of the classical closest-pair problem, aims to store a dataset of points in some data structure such that whenever a query range Q is given, the closest-pair inside Q can be reported efficiently. In this paper, we study the approximate version of the RCP problem with two approximation criteria. The first criterion is in terms of the query range, which allows the returned answer to be slight outside the specified query range. The second criterion is in terms of the quality of the answer, which allows the returned pair to be slightly more distant than the true answer. We establish some interesting connections between the approximate RCP problem (with the above two criteria) and classical range-search problems, namely, range reporting and range minimum, by giving general reductions between them.

作为经典最近对问题的范围搜索版本，范围最近对（RCP）问题旨在将点的数据集存储在某些数据结构中，以便每当给出查询范围Q时，内部的最近对问可以有效地报告。在本文中，我们使用两个近似标准研究RCP问题的近似版本。第一个标准是关于查询范围的，这允许返回的答案稍微超出指定的查询范围。第二个标准是根据答案的质量，它使返回的配对对的距离比真正的答案稍远。通过给出近似的RCP问题（具有上述两个标准）和经典的范围搜索问题，即范围报告和范围最小值，我们建立了一些有趣的联系。