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.
CITATION STYLE
Chazelle, B., Drysdale, R. L., & Lee, D. T. (1984). Computing the largest empty rectangle. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 166 LNCS, pp. 43–54). Springer Verlag. https://doi.org/10.1007/3-540-12920-0_4
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