In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criteria. One is the distance criterion, and the other is the recall criterion. All former algorithms suffer the problem that there are no theoretical guarantees for the two approximation criteria. The algorithm proposed in this paper unifies the two kinds of approximation criteria, and has full theoretical guarantees. Furthermore, the query time of the algorithm is sub-linear. As far as we know, it is the first algorithm that achieves both sub-linear query time and full theoretical approximation guarantee.

中文翻译：

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具有完全质量保证的近似k最近邻的亚线性时间算法

在本文中，我们提出了一种近似k最近邻问题的算法。根据现有研究，存在两种近似准则。一个是距离标准，另一个是召回标准。所有以前的算法都存在以下问题：两个近似准则没有理论上的保证。本文提出的算法统一了两种近似准则，具有充分的理论保证。此外，该算法的查询时间是次线性的。据我们所知，这是第一个同时实现亚线性查询时间和完全理论逼近保证的算法。