Skip to main content
SpringerLink
Log in

Efficient Construction of UV-Diagram

  • Conference paper
  • First Online:
Advances in Swarm and Computational Intelligence (ICSI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9142))

Included in the following conference series:

  • 1533 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  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. Akopyan, A.V., Zaslavskiĭ, A.A.: Geometry of Conics. Mathematical World, American Mathematical Society (2007)

    Google Scholar 

  3. Aurenhammer, F.: Voronoi diagrams – a survey of a fundamental geometric data structure. ACM Computing Surveys 23(3), 345–405 (1991)

    Article  Google Scholar 

  4. Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with bregman divergences. Journal of Machine Learning Research 6, 1705–1749 (2005)

    MATH  MathSciNet  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. Dwyer, R.A.: A faster divide-and-conquer algorithm for constructing delaunay triangulations. Algorithmica 2, 137–151 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  10. Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: SIGMOD, pp. 47–57. ACM, New Yor (1984)

    Google Scholar 

  11. Hossain, M.Z., Hasan, M., Amin, M.A.: Analysis of efficient construction for uncertain voronoi diagram. http://www.cvcrbd.org/publications

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. O’Rourke, J.: Computational geometry in C, 2nd edn. Cambridge University Press, New York (1998)

    Book  MATH  Google Scholar 

  17. Richter-Gebert, J.: Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry, 1st edn. Springer Publishing Company, New York (2011)

    Book  Google Scholar 

  18. Sember, J., Evans, W.: Guaranteed voronoi diagrams of uncertain sites. In: Canadian Conference on Computational Geometry, Montreal, Canada (2008)

    Google Scholar 

  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)

    Article  Google Scholar 

  20. Su, P., Drysdale, R.L.S.: A comparison of sequential delaunay triangulation algorithms. Computational Geometry 7, 361–385 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    MATH  MathSciNet  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. Computer Vision and Cybernetics Group, Department of Computer Science and Engineering, Independent University Bangladesh, Dhaka, 1229, Bangladesh

    M. Z. Hossain, Mahady Hasan & M. Ashraful Amin

Authors
  1. M. Z. Hossain
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mahady Hasan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Ashraful Amin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Ashraful Amin .

Editor information

Editors and Affiliations

  1. Peking University, Beijing, China

    Ying Tan

  2. Xi'an Jiaotong-Liverpool University, Suzhou, China

    Yuhui Shi

  3. Universidade de Pernambuco, Recife, Brazil

    Fernando Buarque

  4. Instituto Politécnico Nacional, Mexico, Mexico

    Alexander Gelbukh

  5. Indian Statistical Institute, Kolkata, India

    Swagatam Das

  6. University of Pretoria, Pretoria, South Africa

    Andries Engelbrecht

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Hossain, M.Z., Hasan, M., Amin, M.A. (2015). Efficient Construction of UV-Diagram. In: Tan, Y., Shi, Y., Buarque, F., Gelbukh, A., Das, S., Engelbrecht, A. (eds) Advances in Swarm and Computational Intelligence. ICSI 2015. Lecture Notes in Computer Science(), vol 9142. Springer, Cham. https://doi.org/10.1007/978-3-319-20469-7_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-20469-7_35

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20468-0

  • Online ISBN: 978-3-319-20469-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation