A perfect parallel dictionary
We describe new randomized parallel algorithms for the problems of interval allocation, construction of static dictionaries, and maintenance of dynamic dictionaries. All of our algorithms run optimally in constant time with high probability. Our main result is the construction of what we call a perfect dictionary, a scheme that allows p processors implementing a set M in space proportional to ¦M¦ to process batches of p insert, delete, and lookup instructions on M in constant time pet batch.
Our best results are obtained for a new variant of the CRCW PRAM model of computation called the OR PRAM. For other variants of the CRCW PRAM we show slightly weaker results, with some resource bounds increased by a factor of ⊖(logk n), where k ∈ ℕ is fixed but arbitrarily large.
KeywordsHash Function Failure Probability Current Phase Table Size Lookup Operation
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- [BH91]H. Bast and T. Hagerup, Fast and Reliable Parallel Hashing, manuscript. A preliminary version appeared in Proc. 3rd SPAA (1991), pp. 50–61.Google Scholar
- [BV89]O. Berkman and U. Vishkin, Recursive *-Tree Parallel Data-Structure, in Proc. 30th FOCS (1989), pp. 196–202.Google Scholar
- [CV86]R. Cole and U. Vishkin, Deterministic Coin Tossing and Accelerating Cascades: Micro and Macro Techniques for Designing Parallel Algorithms, in Proc. 18th STOC (1986), pp. 206–219.Google Scholar
- [DM92]M. Dietzfelbinger and F. Meyer auf der Heide, Dynamic Hashing in Real Time, in Informatik: Festschrift zum 60. Geburtstag von Günter Hotz (1992), Teubner-Texte zur Informatik, Band 1, Teubner, Stuttgart (a preliminary version appeared in Proc. 17th ICALP (1990), Springer LNCS, Vol. 443, pp. 6–19).Google Scholar
- [GMV91]J. Gil, Y. Matias, and U. Vishkin, Towards a Theory of Nearly Constant Time Parallel Algorithms, in Proc. 32nd FOCS (1991), pp. 698–710.Google Scholar
- [G91]M. T. Goodrich, Using Approximation Algorithms to Design Parallel Algorithms that May Ignore Processor Allocation, in Proc. 32nd FOCS (1991), pp. 711–722.Google Scholar
- [GR87]V. Grolmusz and P. Ragde, Incomparability in Parallel Computation, in Proc. 28th FOCS (1987), pp. 89–98.Google Scholar
- [H91]T. Hagerup, Fast Parallel Space Allocation, Estimation and Integer Sorting, Tech. Rep. No. MPI-I-91-106 (1991), Max-Planck-Institut für Informatik, Saarbrücken.Google Scholar
- [M92]P. D. MacKenzie, Load Balancing Requires Ω(log* n) Expected Time, in Proc. 3rd SODA (1992), pp. 94–99.Google Scholar