Space-efficient algorithm for computing a centerpoint of a set of points in R2

We study a space-efficient algorithm for computing a centerpoint for a set P of n points in R2, where the points in P are given in a read-only array. We propose an algorithm that finds a centerpoint of P in O(T(n2)log3⁡n) time using O(S(n2)) extra space, where T(n) and S(n) are the time and extra space complexities of computing the median among a set of n elements stored in a read-only array. We also present the applications of this algorithm for computing the Tukey depth and k-hull of a point set in R2.