Abstract
In this paper, following results are obtained :
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1.
N numbers of m bits can be added in time O(lg N/lg(lg N)+lg m) with O( (m*N1−(c/lglg N))*(lglg N/lg2N) + (N*lglg N/lg N) ) processors. Here, c is some pre-assigned constant (lg N is lg2 N).
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2.
O(N lglg N/lg N) processors are sufficient to add O(Nc/lglg N) bit numbers in θ(lg N/lglg N) time. Thus, the algorithm achieves optimal (linear) speed-up.
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3.
An algorithm to add N-bit numbers in O(lg N/lglg N) time if all bits of a number can be set independently in parallel.
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4.
With N1+(1/lglg N) processors it is possible to sort in θ(lg N/lglg N) time.
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5.
N numbers can be sorted in O(lg N/lglg M) time using O(N*M) processors (if lg M/lglg M ≥ lglg N).
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© 1988 Springer-Verlag Berlin Heidelberg
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Saxena, S., Bhatt, P.C.P., Prasad, V.C. (1988). On parallel sorting and addition with concurrent writes. In: Nori, K.V., Kumar, S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1988. Lecture Notes in Computer Science, vol 338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50517-2_77
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DOI: https://doi.org/10.1007/3-540-50517-2_77
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