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 2βs+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, 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 et al. , our structure uses simpler certificates, uses roughly the same resources, and is also dynamic.
|Number of pages||13|
|Journal||Lecture Notes in Computer Science|
|State||Published - 2005|
|Event||9th International Workshop on Algorithms and Data Structures, WADS 2005 - Waterloo, Canada|
Duration: 15 Aug 2005 → 17 Aug 2005