[R] Find a rectangle of maximal area

[Jim Lemon]

On 03/21/2010 10:12 PM, Hans W Borchers wrote:
> For an application in image processing -- using R for statistical purposes -- I
> need to solve the following task:
>
> Given n (e.g. n = 100 or 200) points in the unit square, more or less randomly
> distributed. Find a rectangle of maximal area within the square that does not
> contain any of these points in its interior.
>
> If a, b are height and width of the rectangel, other constraints may have to be
> imposed such as  a, b<= 0.5  and/or  0.5<= a/b<= 2.0 . The rectangle is
> allowed to touch the border of the square.
>
> For each new image the points will be identified by the application, like all
> stars of a certain brightness on an astronomical picture. So the task will have
> to be performed several times.
>
> I assume this problem is computationally hard. I would like to find a solution
> that is reasonably fast for  n = 100..200  points. Exhaustive search along the
> x, y coordinates of the points will not be fast enough.
>
> I know this request is not about R syntax and does not contain 'repro-code'. But
> perhaps a somehow similar problem has been solved before.
>
Hi Hans,
The emptyspace function in the plotrix package is a fairly crude 
implementation of this, but the code might give you some ideas.

Jim