On the construction of abstract voronoi diagrams
نویسندگان
چکیده
منابع مشابه
On the Construction of Abstract Voronoi Diagrams
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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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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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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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...
متن کاملAbstract Voronoi diagrams revisited
Voronoi Diagrams Revisited Rolf Klein∗ Elmar Langetepe∗ Zahra Nilforoushan† Abstract Abstract Voronoi diagrams [21] were designed as a unifying concept that should include as many concrete types of diagrams as possible. To ensure that abstract Voronoi diagrams, built from given sets of bisecting curves, are finite graphs, it was required that any two bisecting curves intersect only finitely oft...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1991
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02574686