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

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

A Sub-linear Time Algorithm for Approximating k-Nearest-Neighbor with Full Quality Guarantee

In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criterion. One is the distance criteria, and the other is the recall criteria. All former algorithms suffer the problem that there are no theoretical guarantees for the two approximation criterion. The algorithm proposed in this paper unifies the two kinds of approximation criterion, and has full theoretical guarantees. Furthermore, the query time of the algorithm is sub-linear. As far as we know, it is the first algorithm that achieves both sub-linear query time and full theoretical approximation guarantee