Computation of Non-dominated Points Using Compact Voronoi Diagrams

  • Binay Bhattacharya
  • Arijit Bishnu
  • Otfried Cheong
  • Sandip Das
  • Arindam Karmakar
  • Jack Snoeyink
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)


We discuss in this paper a method of finding skyline or non-dominated points in a set P of n points with respect to a set S of m sites. A point p i  ∈ P is non-dominated if and only if for each p j  ∈ P, \(j \not= i\), there exists at least one point s ∈ S that is closer to p i than p j . We reduce this problem of determining non-dominated points to the problem of finding sites that have non-empty cells in an additively weighted Voronoi diagram under convex distance function. The weights of the said Voronoi diagram are derived from the co-ordinates of the points of P and the convex distance function is derived from S. In the 2-dimensional plane, this reduction gives a O((m + n)logm + n logn)-time randomized incremental algorithm to find the non-dominated points.


Voronoi Diagram Query Point Voronoi Cell Additive Weight Lower Envelope 
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  1. 1.
    Borzsonyi, S., Kossmann, D., Stocker, K.: The skyline operator. In: Proceedings of the 17th International Conference on Data Engineering, Washington, DC, USA, pp. 421–430. IEEE Computer Society, Los Alamitos (2001)CrossRefGoogle Scholar
  2. 2.
    Brown, K.Q.: Geometric transforms for fast geometric algorithms. Ph.D. thesis, Dept. Comput. Sci., Carnegie-Mellon Univ., Pittsburgh, PA, Report CMU-CS-80-101 (1980)Google Scholar
  3. 3.
    Cassels, J.: An Introduction to the Geometry of Numbers. Springer, Heidelberg (1959)zbMATHGoogle Scholar
  4. 4.
    Chomicki, J., Godfrey, P., Gryz, J., Liang, D.: Skyline with presorting. In: Proceedings of the 17th International Conference on Data Engineering, Washington, DC, USA, pp. 717–816. IEEE Computer Society, Los Alamitos (2003)Google Scholar
  5. 5.
    Kirkpatrick, D., Snoeyink, J.: Tentative prune-and-search for computing fixed-points with applications to geometric computation. Fundam. Inform. 22, 353–370 (1995)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Klein, R.: Concrete and Abstract Voronoi Diagrams. LNCS, vol. 400. Springer, Heidelberg (1989)zbMATHGoogle Scholar
  7. 7.
    Kossmann, D., Ramsak, F., Rost, S.: Shooting stars in the sky: An online algorithm for skyline queries. In: Proceedings of VLDB, pp. 275–286 (2002)Google Scholar
  8. 8.
    McAllister, M., Kirkpatrick, D., Snoeyink, J.: A compact piecewise-linear Voronoi diagram for convex sites in the plane. Discrete Comput. Geom. 15, 73–105 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Papadias, D., Tao, Y., Fu, G., Seeger, B.: Progressive skyline computation in database systems. ACM Transaction on Database System 30(1), 41–82 (2005)CrossRefGoogle Scholar
  10. 10.
    Sack, J.-R., Urrutia, J.: Handbook of computational geometry. North-Holland Publishing Co., Amsterdam (2000)zbMATHGoogle Scholar
  11. 11.
    Sharifzadeh, M., Shahabi, C.: The spatial skyline queries. In: VLDB 2006: Proceedings of the 32nd international conference on Very large data bases, pp. 751–762. VLDB Endowment (2006)Google Scholar
  12. 12.
    Son, W., Lee, M.-W., Ahn, H.-K., Hwang, S.w.: Spatial skyline queries: An efficient geometric algorithm. CoRR, abs/0903.3072 (2009)Google Scholar
  13. 13.
    Tan, K.-L., Eng, P.-K., Ooi, B.C.: Efficient progressive skyline computation. In: VLDB 2001: Proceedings of the 27th International Conference on Very Large Data Bases, pp. 301–310. Morgan Kaufmann Publishers Inc., San Francisco (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Binay Bhattacharya
    • 1
  • Arijit Bishnu
    • 2
  • Otfried Cheong
    • 3
  • Sandip Das
    • 2
  • Arindam Karmakar
    • 2
  • Jack Snoeyink
    • 4
  1. 1.School of Computing ScienceSimon Fraser UniversityCanada
  2. 2.Advanced Computing and Microelectronics UnitIndian Statistical InstituteKolkataIndia
  3. 3.Department of Computer ScienceKorea Advanced Institute of Science and TechnologyDaejeonKorea
  4. 4.Department of Computer ScienceUniversity of North Carolina at Chapel HillUSA

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