Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. Given a set of points S and a radius parameter r > 0, the rnear neighbor (r-NN) problem asks for a data structure that, given any query point q, returns a point p within distance at most r from q. In this paper, we study the r-NN problem in the light of individual fairness and providing equal opportunities: all points that are within distance r from the query should have the same probability to be returned. In the low-dimensional case, this problem was first studied by Hu, Qiao, and Tao (PODS 2014). Locality sensitive hashing (LSH), the theoretically strongest approach to similarity search in high dimensions, does not provide such a fairness guarantee.

中文翻译：

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通过采样进行公平近邻搜索

相似性搜索是一种基本的算法原语，广泛用于许多计算机科学学科。给定一组点 S 和一个半径参数 r > 0，近邻 (r-NN) 问题要求一个数据结构，在给定任何查询点 q 的情况下，返回一个点 p，它与 q 的距离最多为 r。在本文中，我们从个体公平性和提供平等机会的角度研究 r-NN 问题：与查询距离 r 内的所有点应该具有相同的返回概率。在低维情况下，这个问题首先由 Hu、Qiao 和 Tao 研究（PODS 2014）。局部敏感散列（LSH），理论上最强的高维相似性搜索方法，不提供这样的公平保证。