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- W4288335218 abstract "$newcommand{ball}{mathbb{B}}newcommand{dsQ}{{mathcal{Q}}}newcommand{dsS}{{mathcal{S}}}$In this work we study a fair variant of the near neighbor problem. Namely, given a set of $n$ points $P$ and a parameter $r$, the goal is to preprocess the points, such that given a query point $q$, any point in the $r$-neighborhood of the query, i.e., $ball(q,r)$, have the same probability of being reported as the near neighbor. We show that LSH based algorithms can be made fair, without a significant loss in efficiency. Specifically, we show an algorithm that reports a point in the $r$-neighborhood of a query $q$ with almost uniform probability. The query time is proportional to $Obigl( mathrm{dns}(q.r) dsQ(n,c) bigr)$, and its space is $O(dsS(n,c))$, where $dsQ(n,c)$ and $dsS(n,c)$ are the query time and space of an LSH algorithm for $c$-approximate near neighbor, and $mathrm{dns}(q,r)$ is a function of the local density around $q$. 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. Finally, we run experiments to show performance of our approach on real data." @default.
- W4288335218 created "2022-07-29" @default.
- W4288335218 creator A5040577923 @default.
- W4288335218 creator A5065331345 @default.
- W4288335218 date "2019-06-06" @default.
- W4288335218 modified "2023-09-30" @default.
- W4288335218 title "Near Neighbor: Who is the Fairest of Them All?" @default.
- W4288335218 doi "https://doi.org/10.48550/arxiv.1906.02640" @default.
- W4288335218 hasPublicationYear "2019" @default.
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