Variations of Enclosing Problem Using Axis Parallel Square(s): A General Approach

摘要

Let P be a set of n?points in two dimensional plane. For each point , we locate an axis- parallel unit square having one particular side passing through p and enclosing the maximum number of points from P. Considering all points , such n?squares can be reported in O(nlogn)?time. We show that this result can be used to (i) locate m>(2)?axis-parallel unit squares which are pairwise disjoint and they together enclose the maximum number of points from P (if exists) and (ii) find the smallest axis-parallel square enclosing at least k points of P , .