Abstract
We present a new data structure, the Leafary tree, for designing an efficient randomized algorithm for the Closest Pair Problem. Using this data structure, we show that the Closest Pair of n points in D-dimensional space, where, D≥2, is a fixed constant, can be found in O(n log n/log log n) expected time. The algorithm does not employ hashing.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Dietzfelbinger, M., Hagerup, T., Katajainen, J., Penttonen, M.: A reliable randomized algorithm for the Closest-pair problem, Technical report, Personal Communication.
Dietzfelbinger, M., Meyer auf der Heide, F.: A new universal class of hash functions and dynamic hashing in real time, Proc. ICALP 90, Lecture Notes in Computer Science, Vol. 443, Springer-Verlag, Berlin, 1990, 6–19.
Fortune, S., Hopcroft, J.: A note on Rabin's Nearest-Neighbor algorithm, Information Processing Letters, Vol 8, No 1, (1979), 20–23.
Golin, M., Raman, R., Schwarz, C., Smid, M.: Simple Randomized Algorithms for Closest Pair Problems, Technical Report, Max-Planck-Institut FĂ¼r Informatik, Saarbrucken, Germany, 1992.
Khuller, S., Matias, Y.: A simple randomized sieve algorithm for the closest pair problem, Proc. Third Canadian Conference on Computational Geometry, (1991), 130–134.
Preparata, F.P., Shamos, M.I.: Computational Geometry — an Introduction, Springer-Verlag, New York, 1985.
Rabin, M.: Probabilistic algorithms in Algorithms and Complexity: New directions and Recent results (J.F. Traub ed.), (1976), pp 21–39.
Schwarz, C: Data Structures and Algorithms for the Dynamic Closest Pair Problem, Thesis, Max Planck Institut, SaarbrĂ¼cken, Germany.
Seidel, R.: Backwards Analysis of Randomized Geometric Algorithms, Report TR-92-014, Department of Computer Scince, University of California Berkeley, Berkeley, CA, (1992).
Willard, D.E.: Application of Fusion tree method to computational Geometry and searching, Proceedings of the SODA, 1992, 286–295.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kamakoti, V., Krithivasan, K., Rangan, C.P. (1995). Efficient randomized incremental algorithm for the closest pair problem using Leafary trees. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030821
Download citation
DOI: https://doi.org/10.1007/BFb0030821
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60216-3
Online ISBN: 978-3-540-44733-7
eBook Packages: Springer Book Archive