SIAM Journal on Computing
Department of Computer Science
We consider the following problem: Given a rectangle containing N points, find the largest area subrectangle with sides parallel to those of the original rectangle which contains none of the given points. If the rectangle is a piece of fabric or sheet metal and the points are flaws, this problem is finding the largest-area rectangular piece which can be salvaged. A previously known result  takes $O(N^2 )$ worst-case and $O(N\log ^2 N)$ expected time. This paper presents an $O(N\log ^3 N)$ time, $O(N\log N)$ space algorithm to solve this problem. It uses a divide-and-conquer approach similar to the ones used by Bentley  and introduces a new notion of Voronoi diagram along with a method for efficient computation of certain functions over paths of a tree.
Dartmouth Digital Commons Citation
Chazelle, B.; Drysdale, R. L.; and Lee, D. T., "Computing the Largest Empty Rectangle" (1986). Dartmouth Scholarship. 2070.