Abstract
The dynamic closest pair problem is to find the closest pair among a set of points that is continuously being changed by insertions and deletions. In this paper we present a simple, robust, easily coded heuristic for solving the planar closest pair problem. We prove that this heuristic uses only O(log n) expected time to perform an insertion or deletion when the input points are chosen from a very wide class of distributions in the plane.
This work was supported by a Chateaubriand fellowship from the French Ministère des Affaires Étrangères, by the European Community, Esprit II Basic Research Action Number 3075 (ALCOM) and by NSF grant CCR-8918152
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
A. Aho, J. Hopcroft and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass. (1974)
J. L. Bentley and C. H. Papadimitriou, “A Worst-Case Analysis of Nearest-Neighbor Searching by Projection,” 7th Int. Conf. on Automata, Languages and Programming, (August 1980) 470–482.
J.L. Bentley, B.W. Weide, and A.C. Yao, “Optimal Expected-Time Algorithms for Closest Point Problems,” ACM Trans. on Mathematical Software, 6(4) (Dec. 1980) 563–580.
Luc Devroye, Non-Uniform Random Variate Generation, Springer-Verlag, New York. (1986).
M. J. Golin Probabilistic Analysis of Geometric Algorithms (Thesis), Princeton University Technical Report CS-TR-266-90. June 1990.
Torben Hagerup and Christine Rub, “A Guided Tour of Chernoff Bounds,” Information Processing Letters, 33 (1989/90) 305–308.
Klaus Hinrichs, Jurg Nievergelt, and Peter Schorn, “Plane-Sweep Solves the Closest Pair Problem Elegantly,” Information Processing Letters, 26 (January 11, 1988) 255–261.
M. H. Overmars, The Design of Dynamic Data Structures, Lecture Notes in Computer Science, volume 156, Springer-Verlag, Berlin. (1983).
F. P. Preparata and M. I. Shamos Computational Geometry: An Introduction, Springer-Verlag, New York. (1985).
M.O. Rabin, “Probabilistic Algorithms,” Algorithms and Complexity: New Directions and Recent Results (J.F. Traub ed.), (1976) 21–39.
C. Schwarz, M. Smid, and J. Snoeyink, “An Optimal Algorithm for the On-Line Closest Pair Problem,” 8'th ACM Symposium on Computational Geometry, 1992.
Michael Ian Shamos, “Computational Geometry,” Thesis (Yale), (1978).
Michiel Smid, “Maintaining the Minimal Distance of a Point Set in less than Linear time Algorithms Review,” 2(1) (May 1991) 33–44.
Michiel Smid, “Maintaining the Minimal Distance of a Point Set in Polylogarithmic Time (revised version)” Technical report MOI-I-91-103, Max Planck Institut, Saarbrucken, April 1991
Bruce W. Weide, “Statistical Methods in Algorithm Design and Analysis,” Thesis (Carnige-Mellon University). CMU-CS-78-142, (August 1978).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Golin, M.J. (1992). Dynamic closest pairs — A probabilistic approach. In: Nurmi, O., Ukkonen, E. (eds) Algorithm Theory — SWAT '92. SWAT 1992. Lecture Notes in Computer Science, vol 621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55706-7_31
Download citation
DOI: https://doi.org/10.1007/3-540-55706-7_31
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55706-7
Online ISBN: 978-3-540-47275-9
eBook Packages: Springer Book Archive