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Given a set R of n red points and a set B of m blue points, we study theproblem of finding a rectangle that contains all the red points, the minimumnumber of blue points and has the largest area. We call such rectangle amaximum separating rectangle. We address the planar, axis-aligned (2D) version,and present an O(mlogm+n) time, O(m+n) space algorithm. The running timereduces to O(m + n) if the points are pre-sorted by one of the coordinates. Wefurther prove that our algorithm is optimal in the decision model ofcomputation.

Maximum Area Rectangle Separating Red and Blue Points