  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.
