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Optimal Construction of the City Voronoi Diagram

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Algorithms and Computation (ISAAC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4288))

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Abstract

We address proximity problems in the presence of roads on the L 1 plane. More specifically, we present the first optimal algorithm for constructing the city Voronoi diagram. We apply the continuous Dijkstra paradigm to obtain an optimal algorithm for building a shortest path map for a given source, and then it extends to that for the city Voronoi diagram. Moreover, the algorithm applies to other generalized situations including metric spaces induced by roads and obstacles together.

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References

  1. Abellanas, M., Hurtado, F., Icking, C., Klein, R., Langetepe, E., Ma, L., Palop, B., Sacristán, V.: Proximity problems for time metrics induced by the L 1 metric and isothetic networks. In: IX Encuetros en Geometria Computacional (2001)

    Google Scholar 

  2. Aichholzer, O., Aurenhammer, F., Palop, B.: Quickest paths, straight skeletons, and the city Voronoi diagram. In: Proc. 18th Annu. ACM Sympos. Comput. Geom., pp. 151–159 (2002)

    Google Scholar 

  3. Bae, S.W., Chwa, K.-Y.: Shortest paths and Voronoi diagrams with transportation networks under general distances. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 1007–1018. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Bae, S.W., Chwa, K.-Y.: Voronoi diagrams for a transportation network on the Euclidean plane. Internat. J. Comp. Geom. Appl. 16(2–3), 117–144 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bae, S.W., Kim, J.-H., Chwa, K.-Y.: L 1 shortest paths with isothetic roads. Technical Report CS-TR-2005-241, KAIST (2005)

    Google Scholar 

  6. Görke, R., Wolff, A.: Computing the city Voronoi diagram faster. In: Proc. 21st Euro. Workshop on Comput. Geom., pp. 155–158 (2005)

    Google Scholar 

  7. Mitchell, J.S.B.: L 1 shortest paths among polygonal obstacles in the plane. Algorithmica 8, 55–88 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mitchell, J.S.B.: Shortest paths among obstacles in the plane. Internat. J. Comput. Geom. Appl. 6(3), 309–331 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ostrovsky-Berman, Y.: Computing transportation Voronoi diagrams in optimal time. In: Proc. 21st Euro. Workshop on Comput. Geom., pp. 159–162 (2005)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Div. of Computer Science, Dept. of EECS, Korea Advanced Institute of Science and Technology, Daejeon, Korea

    Sang Won Bae & Kyung-Yong Chwa

  2. Div. of Computer Engineering, Pusan University of Foreign Studies, Busan, Korea

    Jae-Hoon Kim

Authors
  1. Sang Won Bae
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  2. Jae-Hoon Kim
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  3. Kyung-Yong Chwa
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Editor information

Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Japan

    Tetsuo Asano

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© 2006 Springer-Verlag Berlin Heidelberg

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Bae, S.W., Kim, JH., Chwa, KY. (2006). Optimal Construction of the City Voronoi Diagram. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_20

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  • DOI: https://doi.org/10.1007/11940128_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49694-6

  • Online ISBN: 978-3-540-49696-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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