COMPUTING THE LARGEST EMPTY RECTANGLE.

Bernard Chazelle, R. L. Drysdale, D. T. Lee

Research output: Contribution to journalArticle

90 Scopus citations

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 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 and introduces a new notion of Voronoi diagram along with a method for efficient computation of certain functions over paths of a tree.

Original languageEnglish (US)
Pages (from-to)300-315
Number of pages16
JournalSIAM Journal on Computing
Volume15
Issue number1
DOIs
StatePublished - Jan 1 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Mathematics(all)

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