Parallelism in Comparison Problems
01 Sep 1975-SIAM Journal on Computing (Society for Industrial and Applied Mathematics)-Vol. 4, Iss: 3, pp 348-355
TL;DR: The worst-case time complexity of algorithms for multiprocessor computers with binary comparisons as the basic operations is investigated and the algorithm for finding the maximum is shown to be optimal for all values of k and n.
Abstract: The worst-case time complexity of algorithms for multiprocessor computers with binary comparisons as the basic operations is investigated. It is shown that for the problems of finding the maximum, sorting, and merging a pair of sorted lists, if n, the size of the input set, is not less than k, the number of processors, speedups of at least $O(k/\log \log k)$ can be achieved with respect to comparison operations. The algorithm for finding the maximum is shown to be optimal for all values of k and n.
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Cites background from "Parallelism in Comparison Problems"
...For more on speed-ups attainable for particular problems, including problems that are log-space complete for P, see for instance [3,4,10,16,54,58,59,60, 61 ]....
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