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International Symposium on Algorithms and Computation

ISAAC 2005: Algorithms and Computation pp 1007–1018Cite as

Shortest Paths and Voronoi Diagrams with Transportation Networks Under General Distances

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3827))

Abstract

Transportation networks model facilities for fast movement on the plane. A transportation network, together with its underlying distance, induces a new distance. Previously, only the Euclidean and the L 1 distances have been considered as such underlying distances. However, this paper first considers distances induced by general distances and transportation networks, and present a unifying approach to compute Voronoi diagrams under such a general setting. With this approach, we show that an algorithm for convex distances can be easily obtained.

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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. Abellanas, M., Hurtado, F., Icking, C., Klein, R., Langetepe, E., Ma, L., Palop, B., Sacristán, V.: Voronoi diagram for services neighboring a highway. Information Processing Letters 86, 283–288 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Aichholzer, O., Aurenhammer, F., Palop, B.: Quickest paths, straight skeletons, and the city voronoi diagram. In: Proceedings of the 8th SoCG, pp. 151–159 (2002)

    Google Scholar 

  4. Bae, S.W., Chwa, K.-Y.: Voronoi diagrams with a transportation network on the euclidean plane. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 101–112. Springer, Heidelberg (2004), Technical report, Korea Advanced Institute of Science and Technology (2005)

    Chapter  Google Scholar 

  5. Corbalan, A.G., Mazon, M., Recio, T.: Geometry of bisectors for strictly convex distances. International Journal of Computertational Gemoetry and Applications 6(1), 45–58 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dehne, F., Klein, R.: The big sweep: On the power of the wavefront approach to Voronoi diagrams. Algorithmica 17, 19–32 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gewali, L., Meng, A., Mitchell, J.S.B., Ntafos, S.: Path planning in 0/1/ ∞ weighted regions with applications. ORSA J. Comput. 2(3), 253–272 (1990)

    MATH  Google Scholar 

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

    Google Scholar 

  9. Kelly, J.C.: Bitopological spaces. Proc. London Math. Soc. 13(3), 71–89 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  10. Klein, R.: Concrete and Abstract Voronoi Diagrams. LNCS, vol. 400. Springer, Heidelberg (1989)

    MATH  Google Scholar 

  11. Klein, R.: Private communication (2005)

    Google Scholar 

  12. Klein, R., Mehlhorn, K., Meiser, S.: Randomized incremental construction of abstract voronoi diagrams. Computational Geometry: Theory and Applications 3, 157–184 (1993)

    MATH  MathSciNet  Google Scholar 

  13. Klein, R., Wood, D.: Voronoi diagrams based on general metrics in the plane. In: Cori, R., Wirsing, M. (eds.) STACS 1988. LNCS, vol. 294, pp. 281–291. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  14. Ma, L.: Bisectors and Voronoi Diagams for Convex Distance Functions. PhD thesis, Fern Unversität Hagen (2000)

    Google Scholar 

  15. Mehlhorn, K., Meiser, S., O’Dunlaing, C.: On the construction of abstract Voronoi diagrams. Discrete Comput. Geom. 6, 211–224 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mennucci, A.C.G.: On asymmetric distances. Preprint (2004), available at http://cvgmt.sns.it/cgi/get.cgi/papers/and04/

  17. Mitchell, J.S.B.: Shortest paths among obstacles, zero-cost regions, and “roads”. Technical Report 764, School Oper. Res. Indust. Engrg., Cornell Univ., Ithaca, NY (1987)

    Google Scholar 

  18. Palop, B.: Algorithmic problems on proximity and location under metric constraints. PhD thesis, U. Politécnica de Catalunya (2003)

    Google Scholar 

  19. Rinow, W.: Die innere Geometrie der Metrischen Räume. Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen, vol. 105. Springer, Berlin (1961)

    MATH  Google Scholar 

  20. Rowe, N.C.: Roads, rivers, and obstacles: optimal two-dimensional path planning around linear features for a mobile agent. Internat. J. Robot. Res. 9, 67–73 (1990)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Division of Computer Science, Department of EECS, Korea Advanced Institute of Science and Technology, Daejeon, Korea

    Sang Won Bae & Kyung-Yong Chwa

Authors
  1. Sang Won Bae
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  2. Kyung-Yong Chwa
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Editor information

Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon , Hong Kong

    Xiaotie Deng

  2. Department of Computer Science, University of Texas at Dallas, EE/CS Building, 75083, Richardson, TX, USA

    Ding-Zhu Du

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© 2005 Springer-Verlag Berlin Heidelberg

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Bae, S.W., Chwa, KY. (2005). Shortest Paths and Voronoi Diagrams with Transportation Networks Under General Distances. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_100

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  • DOI: https://doi.org/10.1007/11602613_100

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30935-2

  • Online ISBN: 978-3-540-32426-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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