Smallest k-point enclosing rectangle and square of arbitrary orientation

Authors:
Sandip Das;Partha P. Goswami;Subhas C. Nandy
Affiliations:
Indian Statistical Institute, Kolkata 700 108, India;Calcutta University, Kolkata 700 029, India;Indian Statistical Institute, Kolkata 700 108, India
Venue:
Information Processing Letters
Year:
2005

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Abstract

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(n2 logn + 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(n2 logn + kn(n - k)2 logn) time.