An Optimal Algorithm for Range Search on Multidimensional Points

This paper proposes an efficient and novel method to address range search on multidimensional points in θ(t) time, where t is the number of points reported in < space. This is accomplished by introducing a new data structure, called BITS kd-tree. This structure also supports fast updation that takes θ(1) time for insertion and O(logn) time for deletion. The earlier best known algorithm for this problem is O(log n + t) time [5, 15] in the pointer machine model.