$\renewcommand{\Re}{\mathbb{R}}$Recent work showed how to construct nearest-neighbor graphs of linear size, on a given set $P$ of $n$ points in $\Re^d$, such that one can answer approximate nearest-neighbor queries in logarithmic time in the spread. Unfortunately, the spread might be unbounded in $n$, and an interesting theoretical question is how to remove the dependency on the spread. Here, we show how to construct an external linear-size data structure that, combined with the linear-size graph, allows us to answer ANN queries in logarithmic time in $n$.

翻译：$\renewcommand{\Re}{\mathbb{R}}$近期研究展示了如何在给定$d$维实空间$\Re^d$中$n$个点构成的集合$P$上，构建线性规模的最近邻图，使得能够在与扩展率对数相关的时间内回答近似最近邻查询。然而，扩展率可能随$n$无界增长，一个重要的理论问题是如何消除对扩展率的依赖。本文提出一种外部线性规模数据结构的构建方法，该结构与线性规模图相结合，使得我们能够在与$n$对数相关的时间内回答近似最近邻查询。