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Edge-skeletons in arrangements with applications

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Abstract

An edge-skeleton in an arrangementA(H) of a finite set of planes inE 3 is a connected collection of edges inA(H). We give a method that constructs a skeleton inO(√n logn) time per edge. This method implies new and more efficient algorithms for a number of structures in computational geometry including order-k power diagrams inE 2 and space cutting trees inE 3.

We also give a novel method for handling special cases which has the potential to substantially decrease the amount of effort needed to implement geometric algorithms.

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Author notes

  1. H. Edelsbrunner

    Present address: Department of Computer Science, University of Illinois, 1304 West Springfield Avenue, 61801, Urbana, IL, USA

Authors and Affiliations

  1. Institutes for Information Processing, Technical University of Graz, Schiesstattgasse 4a, A-8010, Graz, Austria

    H. Edelsbrunner

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  1. H. Edelsbrunner
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Communicated by B. Chazelle.

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Edelsbrunner, H. Edge-skeletons in arrangements with applications. Algorithmica 1, 93–109 (1986). https://doi.org/10.1007/BF01840438

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  • DOI: https://doi.org/10.1007/BF01840438

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