Out-of-Order Event Processing in Kinetic Data Structures

  • Mohammad Ali Abam
  • Pankaj K. Agarwal
  • Mark de Berg
  • Hai Yu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


We study the problem of designing kinetic data structures (KDS’s for short) when event times cannot be computed exactly and events may be processed in a wrong order. In traditional KDS’s this can lead to major inconsistencies from which the KDS cannot recover. We present more robust KDS’s for the maintenance of two fundamental structures, kinetic sorting and tournament trees, which overcome the difficulty by employing a refined event scheduling and processing technique. We prove that the new event scheduling mechanism leads to a KDS that is correct except for finitely many short time intervals. We analyze the maximum delay of events and the maximum error in the structure, and we experimentally compare our approach to the standard event scheduling mechanism.


Event Time Failure Time Delaunay Triangulation Geometric Error Event Processing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agarwal, P.K., Arge, L., Erickson, J.: Indexing moving points. J. Comput. Syst. Sci. 66, 207–243 (2003)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Agarwal, P.K., Gao, J., Guibas, L.J.: Kinetic medians and kd-trees. In: Proc. 10th European Sympos. on Algorithms, pp. 5–16 (2002)Google Scholar
  3. 3.
    Agarwal, P.K., Guibas, L.J., Hershberger, J., Veach, E.: Maintaining the extent of a moving point set. Discrete Comput. Geom. 26(3), 353–374 (2001)MATHMathSciNetGoogle Scholar
  4. 4.
    Agarwal, P.K., Har-Peled, S., Varadarajan, K.R.: Approximating extent measures of points. J. ACM 51(4), 606–635 (2004)CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Alexandron, G., Kaplan, H., Sharir, M.: Kinetic and dynamic data structures for convex hulls and upper envelopes. In: Proc. 9th Intl. Workshop on Data Structures, pp. 269–281 (2005)Google Scholar
  6. 6.
    Basch, J., Guibas, L.J., Hershberger, J.: Data structures for mobile data. J. Algorithms 31, 1–28 (1999)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Basch, J., Guibas, L.J., Zhang, L.: Proximity problems on moving points. In: Proc. 13th ACM Sympos. Comput. Geom., pp. 344–351 (1997)Google Scholar
  8. 8.
    The CGAL Library, http://www.cgal.org/
  9. 9.
    Collins, G., Akritas, A.: Polynomial real root isolation using Descarte’s rule of signs. In: Proc. 3rd ACM Sympos. Symbol. Algebra. Comput., pp. 272–275 (1976)Google Scholar
  10. 10.
    The Core Library, http://www.cs.nyu.edu/exact/
  11. 11.
    Fortune, S.: Progress in computational geometry. In: Martin, R. (ed.) Directions in Geometric Computing, pp. 81–128. Information Geometers Ltd. (1993)Google Scholar
  12. 12.
    Funke, S., Klein, C., Mehlhorn, K., Schmitt, S.: Controlled perturbation for Delaunay triangulations. In: Proc. 16th ACM-SIAM Sympos. Discrete Algorithms, pp. 1047–1056 (2005)Google Scholar
  13. 13.
    Guibas, L.J.: Algorithms for tracking moving objects. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, 2nd edn. CRC Press, Boca Raton (2004)Google Scholar
  14. 14.
    Guibas, L.J., Karavelas, M.: Interval methods for kinetic simulation. In: Proc. 15th Annu. ACM Sympos. Comput. Geom., pp. 255–264 (1999)Google Scholar
  15. 15.
    Guibas, L.J., Karavelas, M., Russel, D.: A computational framework for handling motion. In: Proc. 6th Workshop on Algorithm Engineering and Experiments, pp. 129–141 (2004)Google Scholar
  16. 16.
    Guibas, L.J., Russel, D.: An empirical comparision of techniques for updating Delaunay triangulations. In: Proc. 20th Annu. Sympos. Comput. Geom., pp. 170–179 (2004)Google Scholar
  17. 17.
    Halperin, D., Shelton, C.: A perturbation scheme for spherical arrangements with application to molecular modeling. Comput. Geom. Theory Appl. 10, 273–287 (1998)MATHMathSciNetGoogle Scholar
  18. 18.
    Jacobson, N.: Basic Algebra I, 2nd edn. W.H. Freeman, New York (1985)MATHGoogle Scholar
  19. 19.
    Milenkovic, V., Sacks, E.: An approximate arrangement algorithm for semi-algebraic curves. In: Proc. 22nd Annu. Sympos. Comput. Geom., pp. 237–246 (2006)Google Scholar
  20. 20.
    Schirra, S.: Robustness and precision issues in geometric computation. In: Sack, J.R., Urrutia, J. (eds.) Handbook of Computational Geometry, pp. 597–632. Elsevier Science, Amsterdam (2000)CrossRefGoogle Scholar
  21. 21.
    Yap, C.: Robust geometric computation. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, 2nd edn. CRC Press, Boca Raton (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mohammad Ali Abam
    • 1
  • Pankaj K. Agarwal
    • 2
  • Mark de Berg
    • 1
  • Hai Yu
    • 2
  1. 1.Department of Mathematics and Computing ScienceTU EindhovenEindhovenThe Netherlands
  2. 2.Department of Computer ScienceDuke UniversityDurhamUSA

Personalised recommendations