Nothing Special   »   [go: up one dir, main page]

skip to main content
10.1007/11841036_56guideproceedingsArticle/Chapter ViewAbstractPublication PagesConference Proceedingsacm-pubtype
Article

Out-of-order event processing in kinetic data structures

Published: 11 September 2006 Publication History

Abstract

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.

References

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

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Guide Proceedings
ESA'06: Proceedings of the 14th conference on Annual European Symposium - Volume 14
September 2006
840 pages
ISBN:3540388753

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 11 September 2006

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 0
    Total Downloads
  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 12 Nov 2024

Other Metrics

Citations

View Options

View options

Get Access

Login options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media