### 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(N^{2}) worst-case 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 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.

Original language | English (US) |
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Title of host publication | STACS 1984 - Symposium of Theoretical Aspects of Computer Science |

Editors | K. Mehlhorn, M. Fontet |

Publisher | Springer Verlag |

Pages | 43-54 |

Number of pages | 12 |

ISBN (Print) | 9783540129202 |

State | Published - Jan 1 1984 |

Externally published | Yes |

Event | 1st Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985 - Paris, France Duration: Apr 11 1984 → Apr 13 1984 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 166 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985 |
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Country | France |

City | Paris |

Period | 4/11/84 → 4/13/84 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*STACS 1984 - Symposium of Theoretical Aspects of Computer Science*(pp. 43-54). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 166 LNCS). Springer Verlag.