Parallel dictionaries on 2–3 trees
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Our model of computation is a parallel computer with k synchronized processors P1,...,Pk sharing a common random access storage, where simultaneous access to the same storage location by two or more processors is not allowed. Suppose a 2–3 tree T with n leaves is implemented in the storage, suppose a1,...,ak are data that may or may not be stored in the leaves, and for all i, 1⩽i⩽k, processor Pi knows ai. We show how to search for a1,..., ak in the tree T, how to insert these data into the tree and how to delete them from the tree in O(log n+log k) steps.
KeywordsSimple Algorithm Sequential Algorithm Side Tree Insertion Algorithm Simultaneous Access
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- [AHU]A. Aho, J. Hopcroft and J.D. Ullman, The design and analysis of computer algorithms, Addison-Wesley, Reading, Massachusetts, 1974.Google Scholar
- [AKS]M. Ajtai, J. Komlos and E. Szemerdi, “An O(n log n) sorting network”, Proc. Fifteenth ACM Symp. on Theory of Computing, 1983, to appear.Google Scholar
- [BS]R. Bayer and M. Schkolnick, “Concurrency of operations on B-Trees”, Acta Informatica 9, 1–21 (1977).Google Scholar
- [FW]S. Fortune and J. Wyllie, “Parallelism in random access machines”, Proc. Tenth ACM Symp. on Theory of Computing, 114–118 (1978).Google Scholar
- [S]Ellis C. Schlatter, “Concurrent search and insertion in 2–3 trees”, Acta Informatica 14, 63–86 (1980).Google Scholar
- [V1]U. Vishkin, “Implementation of simultaneous memory access in models that forbid it”, TR 210, Dept. of Computer Science, Technion, Haifa, Israel (1981), and J. of Algorithms 4, 45–50, (1983).Google Scholar
- [V2]U. Vishkin, “Parallel-Design space Distributed-Implementation space (PDDI) general purpose computer”, RC 9541, IBM T.J. Watson Research Center, Yorktown Heights, N.Y. 10598, 1982.Google Scholar
- [W]H. Wagener, “Parallele Bearbeitung von 2-3-Bäumen”, Diplomarbeit, Fakltät für Mathematik, Universität Bielefeld, 1982.Google Scholar