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Journal ArticleDOI

Parallelism in Comparison Problems

Leslie G. Valiant
- 01 Sep 1975 - 
- Vol. 4, Iss: 3, pp 348-355
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TLDR
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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Citations
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L -infinity interdistance selection by parametric search

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On Parallel Integer Merging

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Book ChapterDOI

Conservative Algorithms for Parallel and Sequential Integer Sorting

TL;DR: A conservative CRCW parallel algorithm for integer sorting which sorts n integers from {0, 1, ..., m−1} in time O(n min(log log n, log log m/log n) using p processors is presented.