### Abstract

Given a fixed distribution of point location queries among the triangles in a triangulation of the plane, a data structure is presented that achieves, within constant multiplicative factors, the entropy bound on the expected point location query time. The data structure is a simple variation of Kirkpatrick's classic planar point location structure [D.G. Kirkpatrick, SIAM J. Comput. 12 (1) (1983) 28-35], and has linear construction costs and space requirements.

Original language | English (US) |
---|---|

Pages (from-to) | 19-22 |

Number of pages | 4 |

Journal | Computational Geometry: Theory and Applications |

Volume | 29 |

Issue number | 1 |

DOIs | |

State | Published - Sep 2004 |

### Fingerprint

### Keywords

- Distribution-sensitive data structures
- Point location

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Computational Mathematics
- Control and Optimization
- Geometry and Topology

### Cite this

*Computational Geometry: Theory and Applications*,

*29*(1), 19-22. https://doi.org/10.1016/j.comgeo.2004.03.010

**Expected asymptotically optimal planar point location.** / Iacono, John.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 29, no. 1, pp. 19-22. https://doi.org/10.1016/j.comgeo.2004.03.010

}

TY - JOUR

T1 - Expected asymptotically optimal planar point location

AU - Iacono, John

PY - 2004/9

Y1 - 2004/9

N2 - Given a fixed distribution of point location queries among the triangles in a triangulation of the plane, a data structure is presented that achieves, within constant multiplicative factors, the entropy bound on the expected point location query time. The data structure is a simple variation of Kirkpatrick's classic planar point location structure [D.G. Kirkpatrick, SIAM J. Comput. 12 (1) (1983) 28-35], and has linear construction costs and space requirements.

AB - Given a fixed distribution of point location queries among the triangles in a triangulation of the plane, a data structure is presented that achieves, within constant multiplicative factors, the entropy bound on the expected point location query time. The data structure is a simple variation of Kirkpatrick's classic planar point location structure [D.G. Kirkpatrick, SIAM J. Comput. 12 (1) (1983) 28-35], and has linear construction costs and space requirements.

KW - Distribution-sensitive data structures

KW - Point location

UR - http://www.scopus.com/inward/record.url?scp=77952708241&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952708241&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2004.03.010

DO - 10.1016/j.comgeo.2004.03.010

M3 - Article

VL - 29

SP - 19

EP - 22

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 1

ER -