Smallest k-point enclosing rectangle and square of arbitrary orientation

Given a set of n points in 2D, the problem of identifying the smallest rectangle of arbitrary orientation, and containing exactly k(?n) points is studied in this paper. The worst case time and space complexities of the proposed algorithm are O(n²logn+nk(n−k)(n−k+logk)) and O(n), respectively. The algorithm is then used to identify the smallest square of arbitrary orientation, and containing exactly k points in O(n²logn+kn²(n−k)logn) time.