Volume 166 of the series Lecture Notes in Computer Science pp 4354
Computing the largest empty rectangle
 B. ChazelleAffiliated withDept. Computer Science, Brown University
 , R. L. DrysdaleIIIAffiliated withDept. Mathematics and Computer Science, Dartmouth College
 , D. T. LeeAffiliated withDept. Electrical Engineering/Computer Science, Northwestern University
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 largestarea rectangular piece which can be salvaged. A previously known result[13] takes O(N^{2}) worstcase and O(Nlog^{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 divideandconquer 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.
 Title
 Computing the largest empty rectangle
 Book Title
 STACS 84
 Book Subtitle
 Symposium of Theoretical Aspects of Computer Science Paris, 11–13, 1984
 Pages
 pp 4354
 Copyright
 1984
 DOI
 10.1007/3540129200_4
 Print ISBN
 9783540129202
 Online ISBN
 9783540388050
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 166
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 B. Chazelle ^{(1)}
 R. L. Drysdale III ^{(2)}
 D. T. Lee ^{(3)}
 Author Affiliations

 1. Dept. Computer Science, Brown University, USA
 2. Dept. Mathematics and Computer Science, Dartmouth College, USA
 3. Dept. Electrical Engineering/Computer Science, Northwestern University, USA
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