Abstract
We consider the problem of maintaining a dynamic weighted binary search tree augmented with a secondary search structure. Although we show that partial rebuilding cannot simultaneously achieve optimal search and update times, we introduce a new technique related to partial building called weighted partial rebuilding, which supports optimal worst-case search times (within a constant factor) for primary keys, O(log n) amortized update times, and efficient amortized reweight times. We also give an example application.
This research was partially supported by an NSERC Postdoctoral Fellowship. Part of this research was performed while the author visited NTT Communication Science Labs, Kyoto, Japan.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
C. R. Aragon and R. G. Seidel. Randomized search trees. In Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, pages 540–545, 1989.
S. W. Bent, D. D. Sleator, and R. E. Tarjan. Biased search trees. SIAM Journal on Computing, 14:545–568, 1985.
V. Estivill-Castro and M. Sherk. Competitiveness and response time in on-line algorithms. In Proceedings of the 2nd International Symposium on Algorithms, pages 284–293, 1991.
G. Frederickson and S. Rodger. A new approach to the dynamic maintenance of maximal points in the plane. In Proceedings of the 25th Annual Allerton Conference on Communication, Control, and Computing, pages 879–888, 1987.
R. Klein, O. Nurmi, T. Ottmann, and D. Wood. A dynamic fixed windowing problem. Algorithmica, 4:535–550, 1989.
T. W. Lai and D. Wood. Adaptive heuristics for binary search trees and constant linkage cost. In Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, pages 72–77, 1991.
E. M. McCreight. Priority search trees. SIAM Journal on Computing, 14:257–276, 1985.
K. Mehlhorn. Dynamic binary search. SIAM Journal on Computing, 8:175–198, 1979.
M. H. Overmars and J. van Leeuwen. Dynamic multi-dimensional data structures based on quad-and k-d trees. Acta Informatica, 17:267–285, 1982.
N. Sarnak and R. E. Tarjan. Planar point location using persistant search trees. Communications of the ACM, 29:669–679, 1986.
D. D. Sleator and R. E. Tarjan. Self-adjusting binary search trees. Journal of the ACM, 32:652–686, 1985.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lai, T.W. (1992). Self-adjusting augmented search trees. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_61
Download citation
DOI: https://doi.org/10.1007/3-540-56279-6_61
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56279-5
Online ISBN: 978-3-540-47501-9
eBook Packages: Springer Book Archive