## Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality (1998)

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Citations: | 713 - 33 self |

### BibTeX

@INPROCEEDINGS{Indyk98approximatenearest,

author = {Piotr Indyk and Rajeev Motwani},

title = {Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality},

booktitle = {},

year = {1998},

pages = {604--613},

publisher = {}

}

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### Abstract

The nearest neighbor problem is the following: Given a set of n points P = fp 1 ; : : : ; png in some metric space X, preprocess P so as to efficiently answer queries which require finding the point in P closest to a query point q 2 X. We focus on the particularly interesting case of the d-dimensional Euclidean space where X = ! d under some l p norm. Despite decades of effort, the current solutions are far from satisfactory; in fact, for large d, in theory or in practice, they provide little improvement over the brute-force algorithm which compares the query point to each data point. Of late, there has been some interest in the approximate nearest neighbors problem, which is: Find a point p 2 P that is an ffl-approximate nearest neighbor of the query q in that for all p 0 2 P , d(p; q) (1 + ffl)d(p 0 ; q). We present two algorithmic results for the approximate version that significantly improve the known bounds: (a) preprocessing cost polynomial in n and d, and a trul...