Abstract
A new efficient data structure, based on the augmentation technique used in the interpolation search tree by Mehlhorn and Tsakalidis, is presented. We achieve:
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a trade-off between input distribution and search cost for dynamic interpolation search.
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θ(log log n) expected time for search and update operations for a larger class of densities than Mehlhorn and Tsakalidis.
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o(log log n) expected time for search and update operations for a large class of densities. As an example, we give an unbounded density for which we achieve θ(log*n) expected time. We also show θ(1) expected time for all bounded densities, in particular, the uniform distribution.
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improved worst-case cost from θ(log2 n) to θ(log n) for searches and from θ(n) to θ(log n) for updates.
We also include a discussion of terminology: which methods should be termed “interpolation search”?
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References
L. Devroye. Lecture Notes on Bucket Algorithms. Birkhäuser, 1985. ISBN 0-8176-3328-6.
G. Frederickson. Implicit Data Structures for the Dictionary Problem. Journal of the ACM, 30(1):80–94, 1983.
G. H. Gonnet. Interpolation and Interplation Hash Searching. PhD thesis, University of Waterloo, February 1977.
A. Itai, A.G. Konheim, and M. Rodeh. A sparse table implementation of priority queues. In Proc. 8th ICALP, pages 417–431, 1981.
K. Mehlhorn and A. Tsakalidis. Dynamic interpolation search. In Proc. 12th ICALP, 1985.
K. Mehlhorn and A. Tsakalidis. Dynamic interpolation search. To appear in Journal of the ACM, 1993.
M. H. Overmars. The Design of Dynamic Data Structures, volume 156 of Lecture Notes in Computer Science. Springer Verlag, 1983. ISBN 3-540-12330-X.
M. H. Overmars and C. Levcopoulos. A balanced search tree with O(1) worst-case update time. Acta Informatica, 26:269–277, 1988.
Y. Perl and E. M. Reingold. Understanding the Complexity of Interpolation Search. Information Processing Letters, 6(6):219–222, December 1977.
W. W. Peterson. Addressing for Random-Access Storage. IBM J. Res. Development, 1 (4):130–146, April 1957.
D. E. Willard. Searching Unindexed and Nonuniformly Generated Files in log log N Time. SIAM Journal on Computing, 14(4), 1985.
A. C. Yao and F. F. Yao. The Complexity of Searching an Ordered Random Table. In Proceeding Seventeenth Annual Symposium on Foundations of Computer Science, pages 173–177, HOUSTON TX, October 1976. IEEE.
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© 1993 Springer-Verlag Berlin Heidelberg
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Andersson, A., Mattsson, C. (1993). Dynamic interpolation search in o(log log n) time. In: Lingas, A., Karlsson, R., Carlsson, S. (eds) Automata, Languages and Programming. ICALP 1993. Lecture Notes in Computer Science, vol 700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56939-1_58
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DOI: https://doi.org/10.1007/3-540-56939-1_58
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