# Adaptive Estimation for Approximate k-Nearest-Neighbor Computations

arXiv: https://arxiv.org/abs/1902.09465 · HTML: https://mlsanity.com/paper/1902.09465/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2019.

## Built on by (most cited first, 5 of 5)

- [Approximate Function Evaluation via Multi-Armed Bandits](https://mlsanity.com/paper/2203.10124/) (2022)
- [BanditPAM++: Faster k-medoids Clustering](https://mlsanity.com/paper/2310.18844/) (2023)
- [Adaptive k-nearest neighbor classifier based on the local estimation of the shape operator](https://mlsanity.com/paper/2409.05084/) (2024)
- [Adaptive Data Depth via Multi-Armed Bandits](https://mlsanity.com/paper/2211.03985/) (2022)
- [UpANNS: Enhancing Billion-Scale ANNS Efficiency with Real-World PIM Architecture](https://mlsanity.com/paper/2410.23805/) (2024)

## Abstract (arXiv)

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 naive method.