## Abstract

Let S be a set of n moving points in the plane. We present a kinetic and dynamic (randomized) data structure for maintaining the convex hull of S. The structure uses O(n) space, and processes an expected number of O( ^{n2}βs+ _{2}(n)logn) critical events, each in O( ^{log2}n) expected time, including O(n) insertions, deletions, and changes in the flight plans of the points. Here s is the maximum number of times where any specific triple of points can become collinear, ^{βs}(q) = ^{λs}(q)/q, and ^{λs}(q) is the maximum length of Davenport-Schinzel sequences of order s on n symbols. Compared with the previous solution of Basch, Guibas and Hershberger [J. Basch, L.J. Guibas, J. Hershberger, Data structures for mobile data, J. Algorithms 31 (1999) 1-28], our structure uses simpler certificates, uses roughly the same resources, and is also dynamic.

Original language | English |
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Pages (from-to) | 144-158 |

Number of pages | 15 |

Journal | Computational Geometry: Theory and Applications |

Volume | 36 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2007 |

## Keywords

- Convex hull
- Dynamic data structures
- Kinetic data structures
- Lower envelope
- Treaps