Contibuted Papers


Volume 166 of the series Lecture Notes in Computer Science pp 43-54


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

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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.