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Largest Empty Rectangle among a Point Set

Jeet Chaudhuri6 and Subhas C. Nandy7

(6)  Wipro Limited, Technology Solns, Bangalore, 560034, India
(7)  Indian Statistical Institute, Calcutta, 700 035, India
Abstract
This paper generalizes the classical MER problem in 2D. Given a set P of n points, here a maximal empty rectangle (MER) is defined as a rectangle of arbitrary orientation such that each of its four sides coincides with at least one member of P and the interior of the rectangle is empty. We propose a simple algorithm based on standard data structure to locate largest area MER on the floor. The time and space complexities of our algorithm are O(n 3) and O(n 2) respectively.

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