Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions

@article{Andoni2006NearOptimalHA,
title={Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions},
author={Alexandr Andoni and P. Indyk},
journal={2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)},
year={2006},
pages={459-468}
}

2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)

We present an algorithm for the c-approximate nearest neighbor problem in a d-dimensional Euclidean space, achieving query time of O(dn 1c2/+o(1)) and space O(dn + n1+1c2/+o(1)). This almost matches the lower bound for hashing-based algorithm recently obtained in (R. Motwani et al., 2006). We also obtain a space-efficient version of the algorithm, which uses dn+n logO(1) n space, with a query time of dnO(1/c2). Finally, we discuss practical variants of the algorithms that utilize fast boundedâ€¦Â Expand