## Abstract

We address the problem of designing data structures that allow efficient search for approximate nearest neighbors. More specifically, given a database consisting of a set of vectors in some high dimensional Euclidean space, we want to construct a space-efficient data structure that would allow us to search, given a query vector, for the closest or nearly closest vector in the database. We also address this problem when distances are measured by the L_{1} norm and in the Hamming cube. Significantly improving and extending recent results of Kleinberg, we construct data structures whose size is polynomial in the size of the database and search algorithms that run in time nearly linear or nearly quadratic in the dimension. (Depending on the case, the extra factors are polylogarithmic in the size of the database.)

Original language | American English |
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Pages (from-to) | 457-474 |

Number of pages | 18 |

Journal | SIAM Journal on Computing |

Volume | 30 |

Issue number | 2 |

DOIs | |

State | Published - 2000 |

Externally published | Yes |

## Keywords

- Data structures
- Nearest neighbor search
- Random projections