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.
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Agarwal, P.K., Arge, L., Erickson, J.: Indexing moving points. J. Comput. Syst. Sci. 66, 207–243 (2003)
Agarwal, P.K., Gao, J., Guibas, L.J.: Kinetic medians and kd-trees. In: Proc. 10th European Sympos. on Algorithms, pp. 5–16 (2002)
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)
Agarwal, P.K., Har-Peled, S., Varadarajan, K.R.: Approximating extent measures of points. J. ACM 51(4), 606–635 (2004)
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)
Basch, J., Guibas, L.J., Hershberger, J.: Data structures for mobile data. J. Algorithms 31, 1–28 (1999)
Basch, J., Guibas, L.J., Zhang, L.: Proximity problems on moving points. In: Proc. 13th ACM Sympos. Comput. Geom., pp. 344–351 (1997)
The CGAL Library, http://www.cgal.org/
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)
The Core Library, http://www.cs.nyu.edu/exact/
Fortune, S.: Progress in computational geometry. In: Martin, R. (ed.) Directions in Geometric Computing, pp. 81–128. Information Geometers Ltd. (1993)
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)
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)
Guibas, L.J., Karavelas, M.: Interval methods for kinetic simulation. In: Proc. 15th Annu. ACM Sympos. Comput. Geom., pp. 255–264 (1999)
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)
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)
Halperin, D., Shelton, C.: A perturbation scheme for spherical arrangements with application to molecular modeling. Comput. Geom. Theory Appl. 10, 273–287 (1998)
Jacobson, N.: Basic Algebra I, 2nd edn. W.H. Freeman, New York (1985)
Milenkovic, V., Sacks, E.: An approximate arrangement algorithm for semi-algebraic curves. In: Proc. 22nd Annu. Sympos. Comput. Geom., pp. 237–246 (2006)
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)
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)
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Abam, M.A., Agarwal, P.K., de Berg, M., Yu, H. (2006). Out-of-Order Event Processing in Kinetic Data Structures. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_56
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DOI: https://doi.org/10.1007/11841036_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38875-3
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