Closest Pair Algorithms in 2D space,a commentary on complexity and reductions

One of the most challenging problems in computational geometry is closest pair of points given n points. Brute force algorithms[1] and Divide and conquer[1] have been verified and the lowest complexity of  attributed to latter class of algorithms, with worst case being for the former being . We propose a method of partitioning the set of n-points based on the least area rectangle that can circumscribe these points