New directions in nearest neighbor searching with applications to lattice sieving

To solve the approximate nearest neighbor search problem (NNS) on the sphere, we propose a method using locality-sensitive filters (LSF), with the property that nearby vectors have a higher probability of surviving the same filter than vectors which are far apart. We instantiate the filters using spherical caps of height 1 − α, where a vector survives a filter if it is contained in the corresponding spherical cap, and where ideally each filter has an independent, uniformly random direction. For small α, these filters are very similar to the spherical locality-sensitive hash (LSH) family previously studied by Andoni et al. For larger α bounded away from 0, these filters potentially achieve a superior performance, provided we have access to an efficient oracle for finding relevant filters. Whereas existing LSH schemes are limited by a performance parameter of ρ ≥ 1/(2c2 − 1) to solve approximate NNS with approximation factor c, with spherical LSF we potentially achiev...

• Type: Journal
• Year: 2016
• Where: SODA
• Authors: Anja Becker, Léo Ducas, Nicolas Gama, Thijs Laarhoven
• Keywords: Algorithms, SODA 2016