A general sequential time-space tradeoff for finding unique elements

Authors:
P. Beame
Affiliations:
Computer Science Department, FR-35, University of Washington, Seattle, Washington
Venue:
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Year:
1989

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Abstract

An optimal &OHgr;(n2) lower bound is shown for the time-space product of any R-way branching program that determines those values which occur exactly once in a list of n integers in the range [1, R] where R ≥ n. This &OHgr;(n2) tradeoff also applies to the sorting problem and thus improves the previous time-space tradeoffs for sorting. Because the R-way branching program is a such a powerful model these time-space product tradeoffs also apply to all models of sequential computation that have a fair measure of space such as off-line multi-tape Turing machines and off-line log-cost RAMs.