Randomized range-maxima in nearly-constant parallel time |
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| Authors: | Omer Berkman Yossi Matias Uzi Vishkin |
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| Affiliation: | (1) Dept. of Computer Science, King's College London, Strand, WC2R 2LS London, ENGLAND;(2) Institute for Advanced Computer Studies and Dept. of Electrical Engineering, University of Maryland, 20742 College Park, MD, USA;(3) Institute for Advanced Computer Studies, University of Maryland, 20742 College Park, MD, USA;(4) Dept. of Computer Science, Tel Aviv University, ISRAEL;(5) Present address: AT&T Bell Laboratories, 600 Mountain Avenue, 07974-0636 Murray Hill, NJ, USA |
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| Abstract: | Given an array ofn input numbers, therange-maxima problem is that of preprocessing the data so that queries of the type  what is the maximum value in subarray i..j] can be answered quickly using one processor. We present a randomized preprocessing algorithm that runs inO(log*
n) time with high probability, using an optimal number of processors on a CRCW PRAM; each query can be processed in constant time by one processor. We also present a randomized algorithm for a parallel comparison model. Using an optimal number of processors, the preprocessing algorithm runs inO( (n)) time with high probability; each query can be processed inO ( (n)) time by one processor. (As is standard, (n) is the inverse of Ackermann function.) A constant time query can be achieved by some slowdown in the performance of the preprocessing stage. |
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| Keywords: | parallel algorithms randomized algorithms PRAM comparison model range maximum prefix maximum |
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