### Abstract

Let S be a connected planar polygonal subdivision with n edges and of total area 1. We present a data structure for point location in S where queries with points far away from any region boundary are answered faster. More precisely, we show that point location queries can be answered in time O(1 + min(log 1/Δ_{p}, log n)), where Δ_{p} is the distance of the query point p to the boundary of the region containing p. Our structure is based on the following result: any simple polygon P can be decomposed into a linear number of convex quadrilaterals with the following property: for any point p ∈ P, the quadrilateral containing p has area Ω(δ _{p}^{2}).

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings |

Pages | 49-60 |

Number of pages | 12 |

DOIs | |

State | Published - Aug 12 2013 |

Event | 13th International Symposium on Algorithms and Data Structures, WADS 2013 - London, ON, Canada Duration: Aug 12 2013 → Aug 14 2013 |

### 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 | 8037 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 13th International Symposium on Algorithms and Data Structures, WADS 2013 |
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Country | Canada |

City | London, ON |

Period | 8/12/13 → 8/14/13 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings*(pp. 49-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8037 LNCS). https://doi.org/10.1007/978-3-642-40104-6_5