Maximum-width Axis-Parallel Empty Rectangular Annulus

12/01/2017

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by   Arpita Baral, et al.

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Given a set P of n points on R^2, we address the problem of computing an axis-parallel empty rectangular annulus A of maximum-width 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^3) 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 n) time and O(n) space.