By making appropriate transformations we see that the problem of determining empty rectangles is equivalent to finding maximal points. Bentley et al. 2 Z be a terminal. J. L. Bentley, K. T. Kung, M. Schkolnick, and C. D. Thompson. On the Average Number of Maxima in a Set of Vectors and Applications .
Analogous definitions hold for the other three quadrants with the corresponding sign changes.
The set of maximal vectors forms a superset of the convex hull vectors. If the first part is executed by using the algorithm of Bentley et al. This result remains true for d 2. H.T. Kung, M. Schkolnick, and C.D. Thomson. On the average number of maxima in a set of vectors and applications .