Randomized incremental construction of abstract Voronoi diagrams
نویسندگان
چکیده
منابع مشابه
Randomized Incremental Construction of Abstract Voronoi Diagrams
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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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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We show that the abstract Voronoi diagram of n sites in the plane can be constructed in time O(n log n) by a randomized algorithm. This yields an alternative, but simpler, O(n log n) algorithm in many previously considered cases and the first O(n log n) algorithm in some cases, e.g., disjoint convex sites with the Euclidean distance function. Abstract Voronoi diagrams are given by a family of b...
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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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Abstr:·lct.: Abstra<.l Vomnoi Diagrams are defined by a .y.tem of bL:s.:c l ing curve!! in 'h" plan.,. r~ther than by the concept of d i.s t .. nc" IK88n.bj. Mehlhorn . Meiser . O' Dunla ,,,!: jl\ntOj . howed how to const ruct such diagram .• in time O(n logn) by B randomized al~( ... rithrn if the bisecting cu rve,; "re in general position. In thi. paper we drop the genpra l posit ion as!j ump...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 1993
ISSN: 0925-7721
DOI: 10.1016/0925-7721(93)90033-3