Sampling near neighbors in search for fairness

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  • Martin Aumüller
  • Sariel Har-Peled
  • Sepideh Mahabadi
  • Pagh, Rasmus
  • Francesco Silvestri

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 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. The problem is of special interest in high dimensions, where Locality Sensitive Hashing (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.

TidsskriftCommunications of the ACM
Udgave nummer8
Sider (fra-til)83-90
StatusUdgivet - 2022

Bibliografisk note

Funding Information:
S. Har-Peled was partially supported by a NSF AF award CCF-1907400. R. Pagh is part of BARC, supported by the VILLUM Foundation grant 16582. F. Silvestri was partially supported by PRIN Project n. 20174LF3T8 AHeAD.

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© 2022 ACM.

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