Abstract
We propose a novel method for representing evolving databases by “evolving sets”, which is particularly useful when we are interested in reconstructing any past state of a database. This theoretical framework therefore reduces the problem concerning the history management of databases to the problem of efficiently managing the history of a set evolving in time. We present a dynamic algorithm that reconstructs the state of the set at a given time t in the past in O(|s(t)| + loglogT) time, where |s(t)| is the size of the answer and T is the maximal size of the time interval (t ≤ T). The space used is linear to the number of changes that occurred during the set's evolution. The resulting algorithm is thereby more efficient than all previous methods dealing with the history management of evolving databases. In fact the proposed algorithm is optimal within a constant factor, because a lower bound of Ω(|s(t)| + loglogT) is also proved. Furthermore, if a total of O((logT)1/c) parallel processors is available, where c is a positive constant (c ≥ 1), the above bound is reduced to O(|s(t)|).
This research was supported in part by National Science Foundation Grant CDR 881111.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
M. Ajtai, “A Lower Bound for Finding Predecessors in Yao's Cell Probe Model”, Combinatorica, to appear.
M. Ajtai, M. Fredman, J. Komlos, “Hash Functions for Priority Queues”, 24th IEEE FOCS 1983, pp 299–303.
B. Chazelle, “How to Search in History”, Information and Control, 1985, Vol. 64, pp 77–99.
M. Dietzfelbinger, A. Karlin, K. Mehlhorn, F. Meyer, H. Rohnhert and R. Tarjan, “Dynamic Perfect Hashing: Upper and Lower Bounds”, Proc. 29th IEEE FOCS, 1988.
D.P. Dobkin, J.L. Munro, “Efficient Uses of the Past”, 21st IEEE FOCS, 1980, pp 200–206.
A. Fiat, M. Naor, “Implicit O(1) Probe Search”, manuscript, 1988.
A. Fiat, M. Naor, A. Schaffer, J.P. Schmidt, A. Siegel, “Storing and Searching a Multikey Table”, 20-th ACM STOC, 1988, pp 344–353.
A. Fiat, M. Naor, J.P. Schmidt, A. Siegel, “Non-Oblivious Hashing”, 20-th ACM STOC, 1988, pp 367–376.
M.L. Fredman, J. Komlos, “On the Size of Separating Systems and Families of Perfect Hash Functions”, SIAM J. Alg. Disc. Math., March 1984, Vol.5, No.1, pp 61–68.
M.L. Fredman, J. Komlos, E. Szemeredi, “Storing a Sparse Table with O(1) Worst Case Access Time”, JACM, July 1984, Vol.31, pp 538–544.
M.L. Fredman, M. Saks, “The Cell Probe Complexity of Dynamic Data Structures”, to appear.
G.H. Gonnet, “Expected Length of the Longest Probe Sequence in Hash Code Searching”, JACM, April 1981, Vol.28, No.2, pp 289–304.
K. Melhorn, “Data Structures and Algorithms I: Sorting and Searching”, Springer Verlag, Berlin, Heidelberg, 1984.
J.I. Munro, “Searching a Two Key Table Under a Single Key”, 19-th ACM STOC, 1987, pp 383–387.
M. Overmars, “The Design of Dynamic Data Structures”, Springer Lecture Notes in Comp. Sc. 156, Springer Verlag, Berlin, 1983.
F.P. Preparata, M.I. Shamos, “Computational Geometry, An Introduction”, Springer Verlag, Berlin, 1985.
M. Snir, “On Parallel Searching”, SIAM J. of Computing, Vol. 14, No 3, Aug. 1985, pp 688–708.
V.J. Tsotras, B. Gopinath, “Efficient Algorithms Managing the History of Time-Evolving Forests”, Bellcore Tech. Memo., TM-ARH-013880, 1989.
V.J. Tsotras, B. Gopinath, G. Hart, “A New Bound On Parallel Searching”, IEEE Fourth Annual Symposium on Parallel Processing, April 4–6, 1990, Vol 2, pp 613–622.
L. Valiant, “Parallelism in Comparison Based Problems”, SIAM J. of Computing, Sept. 1975, Vol. 4, No 3, pp 348–355.
P. Van Emde Boas, R. Kaas and E. Zijlstra, “Design and Implementation of an Efficient Priority Queue”, Math. Systems Theory 10, 1977, pp 99–127.
D.E. Willard, “Log-logarithmic Worst case Queries are Possible in Space O(n)”, Information Processing Letters, 1983, Vol 17, pp 81–84.
A.C. Yao, “Should Tables Be Sorted? ”, JACM, July 1981, Vol.28, No.3, pp 615–628.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tsotras, V.J., Gopinath, B. (1990). Efficient algorithms for managing the history of evolving databases. In: Abiteboul, S., Kanellakis, P.C. (eds) ICDT '90. ICDT 1990. Lecture Notes in Computer Science, vol 470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53507-1_75
Download citation
DOI: https://doi.org/10.1007/3-540-53507-1_75
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53507-2
Online ISBN: 978-3-540-46682-6
eBook Packages: Springer Book Archive