Maximum-width Axis-Parallel Empty Rectangular Annulus

Given a set P of n points on R, we address the problem of computing an axis-parallel empty rectangular annulus A of maximumwidth such that no point of P lies inside A but all points of P must lie inside, outside and on the boundaries of two parallel rectangles forming the annulus A. We propose an O(n) time and O(n) space algorithm to solve the problem. In a particular case when the inner rectangle of an axis-parallel empty rectangular annulus reduces to an input point we can solve the problem in O(n log n) time and O(n) space.