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Abstract Voronoi Diagrams

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  • First Online:
Encyclopedia of Algorithms

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Years and Authors of Summarized Original Work

  • 2009; Klein, Langetepe, Nilforoushan

Abstract Voronoi Diagrams, Fig. 1
figure 11 figure 11

Voronoi diagrams of points in the Euclidean and Manhattan metric and of disks (or additively weighted points) in the Euclidean plane

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Recommended Reading

  1. Aurenhammer F, Klein R, Lee DT (2013) Voronoi diagrams and Delaunay triangulations. World Scientific, Singapore

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  2. Bohler C, Cheilaris P, Klein R, Liu CH, Papadopoulou E, Zavershynskyi M (2013) On the complexity of higher order abstract Voronoi diagrams. In: Proceedings of the 40th international colloquium on automata languages and programming, Riga. Lecture notes in computer science, vol 7965, pp 208–219

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  3. Bohler C, Klein R (2013) Abstract Voronoi diagrams with disconnected regions. In: Proceedings of the 24th international symposium on algorithms and computation, Hong Kong. Lecture notes in computer science, vol 8283, pp 306–316

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  4. Bohler C, Klein R, Liu CH (2014) Forest-like abstract Voronoi diagrams in linear time. In: 26th Canadian conference on computational geometry, Halifax

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  5. Boissonnat JD, Wormser C, Yvinec M (2006) Curved Voronoi diagrams. In: Boissonnat JD, Teillaud M (eds) Effective computational geometry for curves and surfaces. Mathematics and visualization. Springer, Berlin/New York, pp 67–116

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  6. Edelsbrunner H, Seidel R (1986) Voronoi diagrams and arrangements. Discret Comput Geom 1:387–421

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  7. Klein R (1989) Concrete and abstract Voronoi diagrams. Lecture notes in computer science, vol 400. Springer, Berlin/New York

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  8. Klein R, Langetepe E, Nilforoushan Z (2009) Abstract Voronoi diagrams revisited. Comput Geom Theory Appl 42(9):885–902

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  9. Klein R, Lingas A (1994) Hamiltonian abstract Voronoi diagrams in linear time. In: Proceedings of the 5th international symposium on algorithms and computation, Beijing. Lecture notes in computer science, vol 834, pp 11–19

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  10. Klein R, Mehlhorn K, Meiser S (1993) Randomized incremental construction of abstract Voronoi diagrams. Comput Geom Theory Appl 3:157–184

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  11. Lê NM (1995) Randomized incremental construction of simple abstract Voronoi diagrams in 3-space. In: Proceedings of the 10th international conference on fundamentals of computation theory, Dresden. Lecture notes in computer science, vol 965, pp 333–342

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  12. Malinauskas KK (2008) Dynamic construction of abstract Voronoi diagrams. J Math Sci 154(2): 214–222

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  13. Mehlhorn K, Meiser S, Rasch R (2009) Furthest site abstract Voronoi diagrams. Int J Comput Geom Appl 11:583–616

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  14. Okabe A, Boots B, Sugihara K, Chiu SN (2000) Spatial tessellations: concepts and applications of Voronoi diagrams. Wiley, Chichester

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Authors and Affiliations

  1. Institute for Computer Science, University of Bonn, Bonn, Germany

    Rolf Klein

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  1. Rolf Klein
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Correspondence to Rolf Klein .

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Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Klein, R. (2016). Abstract Voronoi Diagrams. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_603

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