STACS 1984: STACS 84 pp 43-54

# Computing the largest empty rectangle

• B. Chazelle
• R. L. DrysdaleIII
• D. T. Lee
Contibuted Papers

DOI: 10.1007/3-540-12920-0_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 166)
Cite this paper as:
Chazelle B., Drysdale R.L., Lee D.T. (1984) Computing the largest empty rectangle. In: Fontet M., Mehlhorn K. (eds) STACS 84. STACS 1984. Lecture Notes in Computer Science, vol 166. Springer, Berlin, Heidelberg

## Abstract

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[13] takes O(N2) worst-case and O(Nlog2N) expected time. This paper presents an O(N log3N) time, O(N log N) space algorithm to solve this problem. It uses a divide-and-conquer approach similar to the ones used by Strong and Bentley[1] and introduces a new notion of Voronoi diagram along with a method for efficient computation of certain functions over paths of a tree.

## Authors and Affiliations

• B. Chazelle
• 1
• R. L. DrysdaleIII
• 2
• D. T. Lee
• 3
1. 1.Dept. Computer ScienceBrown UniversityUSA
2. 2.Dept. Mathematics and Computer ScienceDartmouth CollegeUSA
3. 3.Dept. Electrical Engineering/Computer ScienceNorthwestern UniversityUSA