An Algorithm for Reducing Approximate Nearest Neighbor to Approximate Near Neighbor with O(logn) Query Time

TL;DR

This paper introduces a novel reduction algorithm that transforms the Approximate Nearest Neighbor problem into an Approximate Near Neighbor problem, achieving logarithmic query time using a box split method.

Contribution

It presents the first reduction algorithm with O(log n) query time for the problem, improving over previous polylogarithmic methods.

Findings

Achieves O(log n) query time using box split method

Improves efficiency over previous algorithms

Provides theoretical analysis of the reduction process

Abstract

This paper proposes a new algorithm for reducing Approximate Nearest Neighbor problem to Approximate Near Neighbor problem. The advantage of this algorithm is that it achieves O(log n) query time. As a reduction problem, the uery time complexity is the times of invoking the algorithm for Approximate Near Neighbor problem. All former algorithms for the same reduction need polylog(n) query time. A box split method proposed by Vaidya is used in our paper to achieve the O(log n) query time complexity.