## 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(n ^{2}β_{s+2}(n) log n) critical events, each in O(log ^{2} 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, β_{s}(q) = λ_{s}(q)/q, and λ_{s} (q) is the maximum length of Davenport-Schinzel sequences of order s on n symbols. Compared with the previous solution of Basch et al. [2], our structure uses simpler certificates, uses roughly the same resources, and is also dynamic.

Original language | English |
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Pages (from-to) | 269-281 |

Number of pages | 13 |

Journal | Lecture Notes in Computer Science |

Volume | 3608 |

DOIs | |

State | Published - 2005 |

Event | 9th International Workshop on Algorithms and Data Structures, WADS 2005 - Waterloo, Canada Duration: 15 Aug 2005 → 17 Aug 2005 |