Efficient Construction of UV-Diagram

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9142)

Abstract

Construction of the Voronoi diagram for exploring various proximity relations of a given dataset is one of the fundamental problems in numerous application domains. Recent developments in this area allow constructing Voronoi diagram based on the dataset of uncertain objects which is known as Uncertain-Voronoi diagram (UV-diagram). In compare to the conventional Voronoi diagram of point set, the most efficient algorithm known to date for the UV-diagram construction requires extremely long running time because of its sophisticated geometric structure. This text introduces several efficient algorithms and techniques to construct the UV-diagram and compares the advantages and disadvantages with previously known algorithms and techniques in literature.

Keywords

Uncertain-voronoi diagram UV-diagram Uncertain object Voronoi diagram Delaunay triangulation Computational geometry 

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References

  1. 1.
    Agarwal, P.K., Cheng, S.W., Tao, Y., Yi, K.: Indexing uncertain data. In: ACM SIGMOD-SIGACT-SIGART, pp. 137–146. ACM, New York, NY, USA (2009)Google Scholar
  2. 2.
    Akopyan, A.V., Zaslavskiĭ, A.A.: Geometry of Conics. Mathematical World, American Mathematical Society (2007)Google Scholar
  3. 3.
    Aurenhammer, F.: Voronoi diagrams – a survey of a fundamental geometric data structure. ACM Computing Surveys 23(3), 345–405 (1991)CrossRefGoogle Scholar
  4. 4.
    Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with bregman divergences. Journal of Machine Learning Research 6, 1705–1749 (2005)MATHMathSciNetGoogle Scholar
  5. 5.
    Beckmann, N., Kriegel, H.P., Schneider, R., Seeger, B.: The R*-tree: an efficient and robust access method for points and rectangles. In: ACM SIGMOD, pp. 322–331. ACM, New York (1990)Google Scholar
  6. 6.
    Cheng, R., Kalashnikov, D.V., Prabhakar, S.: Querying imprecise data in moving object environments. IEEE Transactions on Knowledge and Data Engineering 16(9), 1112–1127 (2004)CrossRefGoogle Scholar
  7. 7.
    Cheng, R., Xie, X., Yiu, M.L., Chen, J., Sun, L.: UV-diagram: A voronoi diagram for uncertain data. In: ICDE, pp. 796–807. IEEE (2010)Google Scholar
  8. 8.
    Dwyer, R.A.: A faster divide-and-conquer algorithm for constructing delaunay triangulations. Algorithmica 2, 137–151 (1987)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Guibas, L., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of voronoi. ACM Transactions on Graphics 4(2), 74–123 (1985)CrossRefMATHGoogle Scholar
  10. 10.
    Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: SIGMOD, pp. 47–57. ACM, New Yor (1984)Google Scholar
  11. 11.
    Hossain, M.Z., Hasan, M., Amin, M.A.: Analysis of efficient construction for uncertain voronoi diagram. http://www.cvcrbd.org/publications
  12. 12.
    Kao, B., Lee, S.D., Lee, F.K.F., Cheung, D.W., Ho, W.S.: Clustering uncertain data using voronoi diagrams and R-tree index. IEEE Transactions on Knowledge and Data Engineering 22(9), 1219–1233 (2010)CrossRefGoogle Scholar
  13. 13.
    Kuan, J.K.P., Lewis, P.H.: Fast \(k\) nearest neighbour search for R-tree family. In: International Conference on Information, Communications and Signal Processing, vol. 2, pp. 924–928. Singapore (1997)Google Scholar
  14. 14.
    Li, R., Bhanu, B., Ravishankar, C., Kurth, M., Ni, J.: Uncertain spatial data handling: Modeling, indexing and query. Computers & Geosciences 33(1), 42–61 (2007)CrossRefGoogle Scholar
  15. 15.
    Nagy, T.A.: Documentation for the Machine-Readable Version of the Smithsonian Astrophysical Observatory Catalog (EBCDIC Version). Systems and Applied Sciences Corporation R-SAW-7/79-34 (1979)Google Scholar
  16. 16.
    O’Rourke, J.: Computational geometry in C, 2nd edn. Cambridge University Press, New York (1998)CrossRefMATHGoogle Scholar
  17. 17.
    Richter-Gebert, J.: Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry, 1st edn. Springer Publishing Company, New York (2011)CrossRefGoogle Scholar
  18. 18.
    Sember, J., Evans, W.: Guaranteed voronoi diagrams of uncertain sites. In: Canadian Conference on Computational Geometry, Montreal, Canada (2008)Google Scholar
  19. 19.
    Sharifzadeh, M., Shahabi, C.: VoR-Tree: R-trees with voronoi diagrams for efficient processing of spatial nearest neighbor queries. VLDB Endowment 3(1–2), 1231–1242 (2010)CrossRefGoogle Scholar
  20. 20.
    Su, P., Drysdale, R.L.S.: A comparison of sequential delaunay triangulation algorithms. Computational Geometry 7, 361–385 (1997)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Vinh, N.X., Epps, J., Bailey, J.: Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research 11, 2837–2854 (2010)MATHMathSciNetGoogle Scholar
  22. 22.
    Xie, X., Cheng, R., Yiu, M., Sun, L., Chen, J.: UV-diagram: a voronoi diagram for uncertain spatial databases. The VLDB Journal, 1–26 (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • M. Z. Hossain
    • 1
  • Mahady Hasan
    • 1
  • M. Ashraful Amin
    • 1
  1. 1.Computer Vision and Cybernetics Group, Department of Computer Science and EngineeringIndependent University BangladeshDhakaBangladesh

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