## Abstract

Algorithms often carry out equally many computations for “easy” and “hard” problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In this paper, we consider the approximate k-nearest-neighbor problem, which is the problem of finding a subset of O(k) points in a given set of points that contains the set of k nearest neighbors of a given query point. We propose an algorithm based on adaptively estimating the distances, and show that it is essentially optimal out of algorithms that are only allowed to adaptively estimate distances. We then demonstrate both theoretically and experimentally that the algorithm can achieve significant speedups relative to the naïve method.

Original language | English |
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State | Published - 2020 |

Externally published | Yes |

Event | 22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 - Naha, Japan Duration: 16 Apr 2019 → 18 Apr 2019 |

### Conference

Conference | 22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 |
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Country/Territory | Japan |

City | Naha |

Period | 16/04/19 → 18/04/19 |