Abstract
There are many applications where data to be archived have the form of an evolving forest. In this paper we address the problem of efficiently reconstructing the history of a forest evolving in time. A forest is a set of trees and at each time instant a constant number of changes occur in the forest. We propose an optimal, dynamic algorithm that reconstructs the state of any subtree in the forest at a given instant t in the past, in O(|s(t)|+loglogT) time, where |s(t)| is the cardinality of the requested subtree and T is the total length of the evolution. The space used is linear to the total number of changes that occurred during the forest's evolution. If a total of O((logT) 1/c ) parallel processors is available, where c is a constant (c≥1), the loglogT factor is eliminated from the previous time bound. Finally, we optimally address the following query: given a path p in the forest, find all the lifetimes of this path during the forest's evolution.
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.
B. Chazelle, "How to Search in History", Inform. and Control, 1985, Vol. 64, pp 77–99.
B. Chazelle, "Filtering Search: A new Approach to Query Answering", 24th IEEE FOCS, 1983, pp 122–132.
R. Cole, "Searching and Storing Similar Lists", J. Algorithms, Vol 7, 1986, pp 202–220.
M. Dietzfelbinger, A. Karlin, K. Mehlhorn, F. Meyer, H. Rohnhert, R. Tarjan, "Dynamic Perfect Hashing: Upper and Lower Bounds", 29th IEEE FOCS, 1988.
D.P. Dobkin, J.L. Munro, "Efficient Uses of the Past", 21st IEEE FOCS, 1980.
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. Overmars, "The Design of Dynamic Data Structures", Springer Lecture Notes in Comp. Sc. 156, Springer Verlag, Berlin, 1983.
M. Overmars, "Range Searching on a Grid", J. Algorithms, Vol 9, 1988, pp 254–275.
V.J. Tsotras, B. Gopinath, G. Hart, "Optimally Managing the History of an Evolving Forest", TR 177 90-07 CTR-Columbia University, TM Rutgers University, 1990.
V.J. Tsotras, B. Gopinath, "Managing the History of Evolving Sets", submitted for publication, also TR 176 90-06 CTR-Columbia University, TM Rutgers University, 1990.
V.J. Tsotras, B. Gopinath, G. Hart, "A New Bound on Parallel Searching", IEEE 4th Ann. Symp. Parallel Processing, April 4–6, 1990, Vol 2, pp 613–622.
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, 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., Hart, G.W. (1990). Optimally managing the history of an evolving forest. In: Asano, T., Ibaraki, T., Imai, H., Nishizeki, T. (eds) Algorithms. SIGAL 1990. Lecture Notes in Computer Science, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52921-7_96
Download citation
DOI: https://doi.org/10.1007/3-540-52921-7_96
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52921-7
Online ISBN: 978-3-540-47177-6
eBook Packages: Springer Book Archive