A Fast Parallelizable Algorithm for Constructing Balanced Binary Search Trees

We suggest a new non-recursive algorithm for constructing a balanced binary search tree given an array of numbers. The algorithm has O ( N ) time and O (1) auxiliary memory complexity if the given array of N numbers is sorted. The resulting tree is of minimal height and can be transformed into a complete binary search tree while retaining minimal height with O(log N) time and O (1) auxiliary memory. The algorithm allows simple and effective parallelization resulting in time complexity O((N/s)+s+log N) , where s is the number of parallel threads.