Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. Given a set of points S<\/i> and a radius parameter r<\/i> > 0, the r<\/i>-near neighbor (r<\/i>-NN) problem asks for a data structure that, given any query point q<\/i>, returns a point p<\/i> within distance at most r<\/i> from q.<\/i> In this paper, we study the r<\/i>-NN problem in the light of individual fairness and providing equal opportunities: all points that are within distance r<\/i> from the query should have the same probability to be returned. The problem is of special interest in high dimensions, where Locality Sensitive Hashing<\/i> (LSH), the theoretically leading approach to similarity search, does not provide any fairness guarantee. In this work, we show that LSH-based algorithms can be made fair, without a significant loss in efficiency. We propose several efficient data structures for the exact and approximate variants of the fair NN problem. Our approach works more generally for sampling uniformly from a sub-collection of sets of a given collection and can be used in a few other applications. We also carried out an experimental evaluation that highlights the inherent unfairness of existing NN data structures.<\/p>\n","protected":false},"excerpt":{"rendered":"
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 r-near 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 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