### Abstract

Given a set S of n points in the plane, a quadrangulation of S is a planar subdivision whose vertices are the points of S, whose outer face is the convex hull of S, and every face of the subdivision (except possibly the outer face) is a quadrilateral. We show that S admits a quadrangulation if and only if S does not have an odd number of extreme points. If S admits a quadrangulation, we present an algorithm that computes a quadrangulation of S in O(nlogn) time, which is optimal, even in the presence of collinear points. If S does not admit a quadrangulation, then our algorithm can quadrangulate S with the addition of one extra point, which is optimal. Finally, our results imply that a fc-angulation of a set of points can be achieved with the addition of at most k — 3 extra points within the same time bound.

Original language | English (US) |
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Title of host publication | Algorithms and Computations - 6th International Symposium, ISAAC 1995, Proceedings |

Editors | John Staples, Peter Eades, Naoki Katoh, Alistair Moffat |

Publisher | Springer Verlag |

Pages | 372-381 |

Number of pages | 10 |

ISBN (Print) | 3540605738, 9783540605737 |

DOIs | |

State | Published - 1995 |

Event | 6th International Symposium on Algorithms and Computations, ISAAC 1995 - Cairns, Australia Duration: Dec 4 1995 → Dec 6 1995 |

### 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 | 1004 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 6th International Symposium on Algorithms and Computations, ISAAC 1995 |
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Country | Australia |

City | Cairns |

Period | 12/4/95 → 12/6/95 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Computations - 6th International Symposium, ISAAC 1995, Proceedings*(pp. 372-381). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1004). Springer Verlag. https://doi.org/10.1007/bfb0015443