K-enclosing square or rectangle problem revisited

Given a set P of n points in two dimensional plane. In this paper we study the minimum enclosing square problem. First an O(n log² n) time and linear space algorithm is proposed to locate a minimum enclosing axis-parallel square that encloses at least k (1 ≤ k ≤ n) points of P. Then this algorithm is extended to find a minimum enclosing axis parallel square for large values of k (k >; k/2) in O(n+(n-k) log²(n-k)) using O(n) space. These algorithms can also be used to solve the minimum enclosing rectangle problem.