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.
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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
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DOI: https://doi.org/10.1007/3-540-52921-7_96
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