Abstract
In this paper, following results are obtained :
-
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).
-
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.
-
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.
-
4.
With N1+(1/lglg N) processors it is possible to sort in θ(lg N/lglg N) time.
-
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).
Preview
Unable to display preview. Download preview PDF.
References
M.Ajtai,J.Komlos and E.Szemeredi, An O(nlog n) Sorting network, Proc 15th ACM Symposium on Theory of Computing (1983), 1–9.
Y. Azar and U. Vishkin, Tight comparison bounds on the complexity of parallel sorting, SIAM J Computing, 16 (1987), 458–464.
P. Beame, Limits on the power of Concurrent write machines, Info and Contr, 76, (1988) 13–28.
P.Beame and J.Hastad(1987), Optimal Bounds for Decision Problems on the CRCW PRAM, Proc 19th annual ACM Symp on theory of Computing, 83–93.
A. Borodin and J.E. Hopcroft, Routing, Merging and Sorting on Parallel Models of Computation, J. Computer System Sc, 30 (1985), 130–145.
A.K. Chandra,L. Stockmeyer and U. Vishkin, Constant Depth Reducibility, SIAM J Computing, 13 (1984), 423–439.
R.Cole,Parallel Merge Sort,Proc 27th IEEE Annual Symp on Foundations of computer Science (1986),511–516.
R.Cole and U.Vishkin, Faster Optimal Parallel Prefix Sums and list Ranking, Ultra Computer Note #117 & Computer Sc Tech Rept #227, New York University, Feb 1987.
S. Cook, C. Dwork and R. Reischuk, Upper and lower time bounds for Parallel Random Access Machines without Simultaneous writes, SIAM J Computing, 15 (1986), 87–97.
Hastad J, Almost optimal lower bounds for small depth circuits, Proc 18th ACM Symp Theory of Computing (1986), 6–20.
N.Immerman, Expressibility as a Complexity Measure: Results and Directions, Manuscript, 1987.
C.P. Kruskal, Searching, Merging and Sorting in Parallel Computation, IEEE trans Computer, C-32 (1983), 942–946.
C.P. Kruskal,L. Rudolph and M. Snir, The power of Parallel Prefix, IEEE trans Computer, C-34 (1985), 965–968.
M.Li and Y.C.Yesha, New lower bounds for parallel computations, Proc 18th ACM Symposium on Theory of Computing (1986),177–187.
J.F.Rief,An Optimal Algorithm for Integer Sorting,Proc 26th IEEE Annual Symp on Foundations of Computer Sc (1985), 496–504.
S.Saxena,P.C.P.Bhatt and V.C.Prasad, Fastest Possible Parallel Sorting and Addition Algorithms with polynomial number of processors, CSI communications, Dec 1987, 34–35.
L. Stockmeyer and U. Vishkin, Simulation of Parallel Random Access Machines by Circuits, SIAM J Comput, 13 (1984), 409–422.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-50517-2_77
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50517-4
Online ISBN: 978-3-540-46030-5
eBook Packages: Springer Book Archive