### Abstract

We present several efficient dynamic data structures for point-enclosure queries, involving convex fat objects in ℝ^{2} or ℝ^{3}. Our planar structures are actually fitted for a more general class of objects - (β, δ)-covered objects -which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two problems: (i) finding a perfect containment matching between a set of points and a set of convex fat objects, and (ii) finding a piercing set for a collection of convex fat objects, whose size is optimal up to some constant factor.

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

Pages (from-to) | 215-227 |

Number of pages | 13 |

Journal | Computational Geometry: Theory and Applications |

Volume | 15 |

Issue number | 4 |

State | Published - Apr 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

- Containment matching
- Dynamic data structure
- Fat objects
- Piercing set
- Point enclosure

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology

### Cite this

*Computational Geometry: Theory and Applications*,

*15*(4), 215-227.

**Dynamic data structures for fat objects and their applications.** / Efrat, Alon; Katz, Matthew J.; Nielsen, Frank; Sharir, Micha.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 15, no. 4, pp. 215-227.

}

TY - JOUR

T1 - Dynamic data structures for fat objects and their applications

AU - Efrat, Alon

AU - Katz, Matthew J.

AU - Nielsen, Frank

AU - Sharir, Micha

PY - 2000/4

Y1 - 2000/4

N2 - We present several efficient dynamic data structures for point-enclosure queries, involving convex fat objects in ℝ2 or ℝ3. Our planar structures are actually fitted for a more general class of objects - (β, δ)-covered objects -which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two problems: (i) finding a perfect containment matching between a set of points and a set of convex fat objects, and (ii) finding a piercing set for a collection of convex fat objects, whose size is optimal up to some constant factor.

AB - We present several efficient dynamic data structures for point-enclosure queries, involving convex fat objects in ℝ2 or ℝ3. Our planar structures are actually fitted for a more general class of objects - (β, δ)-covered objects -which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two problems: (i) finding a perfect containment matching between a set of points and a set of convex fat objects, and (ii) finding a piercing set for a collection of convex fat objects, whose size is optimal up to some constant factor.

KW - Containment matching

KW - Dynamic data structure

KW - Fat objects

KW - Piercing set

KW - Point enclosure

UR - http://www.scopus.com/inward/record.url?scp=0012741558&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012741558&partnerID=8YFLogxK

M3 - Article

VL - 15

SP - 215

EP - 227

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 4

ER -