Range closest-pair (RCP) search is a range-search variant of the classical closest-pair problem, which aims to store a given set S of points into some space-efficient data structure such that when a query range Q is specified, the closest pair in $S\cap Q$ can be reported quickly. RCP search has received attention over years, but the primary focus was only on ${\mathbb{R}}^2$. In this paper, we study RCP search in higher dimensions. We give the first nontrivial RCP data structures for orthogonal, simplex, halfspace, and ball queries in ${\mathbb{R}}^d$ for any constant d. Furthermore, we prove a conditional lower bound for orthogonal RCP search for $d\ge 3$.

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在更高维度上进行范围最接近的对搜索

距离最近对（RCP）搜索是经典最近对问题的距离搜索变体，其目的是将给定的点集S存储到一些节省空间的数据结构中，以便在指定查询范围Q时，最接近的一对$\mathrm{小号}\cap 问$可以迅速报告。多年来，RCP搜索受到关注，但主要重点仅在于${\mathbb{[R}}^2$。在本文中，我们研究了更高维度的RCP搜索。我们给出了正交，单形，半空间和球形查询中的第一个非平凡RCP数据结构${\mathbb{[R}}^d$对于任何常数d。此外，我们证明了正交RCP搜索的条件下界$d\ge 3$。