Sublinear Explicit Incremental Planar Voronoi Diagrams
نویسندگان
چکیده
منابع مشابه
Incremental Voronoi diagrams
We study the amortized number of combinatorial changes (edge insertions and removals) needed to update the graph structure of the Voronoi diagram VD(S) (and several variants thereof) of a set S of n sites in the plane as sites are added to the set. To that effect, we define a general update operation for planar graphs that can be used to model the incremental construction of several variants of...
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Abstract Voronoi diagrams were introduced by R . Klein [Kle89b, Kle88a, Kle88b] as an axiomatic basis ofVoronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(nlogn) by a randomized algorithm, which is based on Clarkson and Shor's randomized incremental construction technique [CS89]. The new algorithm has the following advantages over previous algorithms: • It can handle...
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Given a tesselation of the plane, defined by a planar straightline graph G, we want to find a minimal set S of points in the plane, such that the Voronoi diagram associated with S ‘fits’ G. This is the Generalized Inverse Voronoi Problem (GIVP), defined in [12] and rediscovered recently in [3]. Here we give an algorithm that solves this problem with a number of points that is linear in the size...
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We present an incremental algorithm for constructing and reconstructing Generalized Voronoi Diagrams (GVDs) on grids. Our algorithm, Dynamic Brushfire, uses techniques from the path planning community to efficiently update GVDs when the underlying environment changes or when new information concerning the environment is received. Dynamic Brushfire is an order of magnitude more efficient than cu...
متن کاملRandomized construction diagrams * incremental of abstract Voronoi Rolf
Abstract Voronoi diagrams were introduced by R. Klein (1988) as an axiomatic basis of Voronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(n log n) by a randomized algorithm, which is based on Clarkson and Shor’s randomized incremental construction technique (1989). The new algorithm has the following advantages over previous algorithms: l It can handle a much wider cl...
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ژورنال
عنوان ژورنال: Journal of Information Processing
سال: 2020
ISSN: 1882-6652
DOI: 10.2197/ipsjjip.28.766