Abstract
Abstract Voronoi diagrams were introduced by R. Klein [14, 11, 12] 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; the algorithm is based on Clarkson and Shor's randomized incremental construction technique [6]. The new algorithm has the following advantages over previous algorithms:
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It can handle a much wider class of abstract Voronoi diagrams than the algorithms presented in [14, 17].
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It can be adapted to a concrete kind of Voronoi diagram by providing a single basic operation, namely the construction of a Voronoi diagram of five sites. Moreover, all geometric decisions are confined to the basic operation, and using this operation, abstract Voronoi diagrams can be constructed in a purely combinatorial manner.
This work was supported partially by the DFG, grants SPP Me 620/6 and Kl 655/2-1, and partially by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (project ALCOM). A preliminary version of this paper was presented at the SIGAL Symposium on Algorithms, Tokyo 1990.
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© 1992 B. G. Teubner Verlagsgesellschaft, Leipzig
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Klein, R., Mehlhorn, K., Meiser, S. (1992). Randomized Incremental Construction of Abstract Voronoi Diagrams. In: Buchmann, J., Ganzinger, H., Paul, W.J. (eds) Informatik. TEUBNER-TEXTE zur Informatik, vol 1. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-95233-2_17
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DOI: https://doi.org/10.1007/978-3-322-95233-2_17
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