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Generalization of Voronoi Diagrams in the Plane
Abstract
In this paper we study the Voronoi diagram for a set of N line segments and circles in the Euclidean plane. The diagram is a generalization of the Voronoi diagram for a set of points in the plane and has applications in wire layout, facility location, clustering and contouring problems. We present an $O(N(\log N)^2 )$ algorithm for constructing the diagram. It is an improvement of a previous known result which takes $O(Nc^{\sqrt {\log N} } )$ time. The algorithm described in this paper is also shown to be applicable under a more general metric if certain conditions are satisfied.
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Cited by
Robot Motion Planning: A Distributed Representation Approach
Barraquand, J., & Latombe, J.-C. (1991) · The International Journal of Robotics Research · doi:10.1177/027836499101000604 · Cited by 995
Generalized delaunay triangulation for planar graphs
Lee, D. T., & Lin, A. K. (1986) · Discrete & Computational Geometry · doi:10.1007/bf02187695 · Cited by 286
Self-citationA Spatial Access-Oriented Implementation of a 3-D GIS Topological Data Model for Urban Entities
Lee, J. (2004) · GeoInformatica · doi:10.1023/b:gein.0000034820.93914.d0 · Cited by 200
Metadata
- Authors
- Lee, D. T., & Drysdale, III
- Venue
- SIAM Journal on Computing
- Published
- 1981-02
- Volume
- 10
- Issue
- 1
- Pages
- 73-87
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2015751084
- Cited by
- 312
- References
- 0
- FWCI
- 6.08
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Generalization of Voronoi Diagrams in the Plane. https://app.cochat.ai/papers/10.1137/0210006
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- Lee, D. T., & Drysdale, III. (1981). Generalization of Voronoi Diagrams in the Plane. SIAM Journal on Computing. https://doi.org/10.1137/0210006
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
