An O(logn) Query Time Algorithm for Reducing ϵ-NN to (c,r)-NN

The problem of reducing ϵ-NN to (c,r)-NN is very important in theoretical computer science area and has attracted many research efforts. In this paper a new algorithm for such problem is proposed, which achieves O(log⁡n) query time. Comparing with the former algorithms for the same problem, this query time is the lowest, which is the main contribution of this paper. The low query time complexity is achieved by raising the preprocessing time and space complexity. How to reduce the cost added into the two complexities is also discussed in this paper.