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Kinetic and Dynamic Data Structures for Convex Hulls and Upper Envelopes (2005)
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| Citations: | 12 - 2 self |
BibTeX
@MISC{Alexandron05kineticand,
author = {Giora Alexandron and et al.},
title = {Kinetic and Dynamic Data Structures for Convex Hulls and Upper Envelopes },
year = {2005}
}
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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)log n) 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 [8], our structure uses simpler certificates, uses roughly the same resources, and is also dynamic.
