On multiplicatively weighted voronoi diagrams for lines in the plane

Kira Vyatkina; Gill Barequet

doi:https://doi.org/10.1007/978-3-642-22619-9_3

On multiplicatively weighted voronoi diagrams for lines in the plane

Kira Vyatkina, Gill Barequet

Computer Science

Technion - Israel Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We describe a method based on the wavefront propagation, which computes a multiplicatively weighted Voronoi diagram for a set L of n lines in the plane in O(n ² logn) time and O(n ²) space. In the process, we derive complexity bounds and certain structural properties of such diagrams. An advantage of our approach over the general purpose machinery, which requires computation of the lower envelope of a set of halfplanes in three-dimensional space, lies in its relative simplicity. Besides, we point out that the unweighted Voronoi diagram for n lines in the plane has a simple structure, and can be obtained in optimal Θ(n ²) time and space.

Original language	English
Title of host publication	Transactions on Computational Science XIII
Editors	Marina Gavrilova, Chih Jeng Kenneth Tan
Pages	44-71
Number of pages	28
DOIs	https://doi.org/10.1007/978-3-642-22619-9_3
State	Published - 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6750 LNCS

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

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https://doi.org/10.1007/978-3-642-22619-9_3

Cite this

Vyatkina, K., & Barequet, G. (2011). On multiplicatively weighted voronoi diagrams for lines in the plane. In M. Gavrilova, & C. J. K. Tan (Eds.), Transactions on Computational Science XIII (pp. 44-71). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6750 LNCS). https://doi.org/10.1007/978-3-642-22619-9_3

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abstract = "We describe a method based on the wavefront propagation, which computes a multiplicatively weighted Voronoi diagram for a set L of n lines in the plane in O(n 2 logn) time and O(n 2) space. In the process, we derive complexity bounds and certain structural properties of such diagrams. An advantage of our approach over the general purpose machinery, which requires computation of the lower envelope of a set of halfplanes in three-dimensional space, lies in its relative simplicity. Besides, we point out that the unweighted Voronoi diagram for n lines in the plane has a simple structure, and can be obtained in optimal Θ(n 2) time and space.",

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Vyatkina, K & Barequet, G 2011, On multiplicatively weighted voronoi diagrams for lines in the plane. in M Gavrilova & CJK Tan (eds), Transactions on Computational Science XIII. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6750 LNCS, pp. 44-71. https://doi.org/10.1007/978-3-642-22619-9_3

On multiplicatively weighted voronoi diagrams for lines in the plane. / Vyatkina, Kira; Barequet, Gill.
Transactions on Computational Science XIII. ed. / Marina Gavrilova; Chih Jeng Kenneth Tan. 2011. p. 44-71 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6750 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Vyatkina K, Barequet G. On multiplicatively weighted voronoi diagrams for lines in the plane. In Gavrilova M, Tan CJK, editors, Transactions on Computational Science XIII. 2011. p. 44-71. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: https://doi.org/10.1007/978-3-642-22619-9_3

On multiplicatively weighted voronoi diagrams for lines in the plane

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