Abstract
We present a conservative CRCW parallel algorithm for integer sorting. This algorithm sorts n integers from {0, 1, ..., m−1} in time O(n log log min(m,n)/p + log n) using p processors. The simulation of our parallel algorithm on the sequential machine yields a sequential 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)).
This author is partially supported by UMKC Faculty Research Grant K-2-11191.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
S. Albers and T. Hagerup. Improved parallel integer sorting without concurrent writing. Proc. The Third Annual ACM-SIAM Symp. on Discrete Algorithms, pp. 463–472.
R. Anderson and G. Miller. Deterministic parallel list ranking. Algorithmica 6: 859–868(1991).
P.C.P. Bhatt, K. Diks, T. Hagerup, V.C. Prasad, T. Radzik, S. Saxena. Improved deterministic parallel integer sorting. Information and Computation 94, 29–47(1991).
M. L. Fredman and D. E. Willard. Blasting through the information theoretic barrier with fusion trees. Proc. 1990 ACM Symp. on Theory of Computing, pp. 1–7(1990).
T. Hagerup. Towards optimal parallel bucket sorting. Inform. and Comput. 75, pp. 39–51(1987).
Y. Han. Designing fast and efficient parallel algorithms. Ph.D. Thesis. Department of Computer Science, Duke University, Durham, North Carolina, 1987.
Y. Han. Parallel algorithms for computing linked list prefix. J. of Parallel and Distributed Computing 6 537–557(1989).
T. Hagerup and H. Shen. Improved nonconservative sequential and parallel integer sorting. Infom. Process. Lett. 36, pp. 57–63(1990).
D. Kirkpatrick and S. Reisch. Upper bounds for sorting integers on random access machines. Theoretical Computer Science 28, pp. 263–276(1984).
P. M. Kogge and H. S. Stone. A parallel algorithm for the efficient solution of a general class of recurrence equations. IEEE Trans. Comput., Vol C-22, pp. 786–792(Aug. 1973).
R. E. Ladner and M. J. Fischer. Parallel prefix computation. J. ACM, pp. 831–838(Oct. 1980).
F. Preparata. New parallel-sorting schemes. IEEE Transactions on Computers, Vol. c-27, No. 7, pp. 669–673(July 1978).
S. Rajasekaran and J. Reif. Optimal and sublogarithmic time randomized parallel sorting algorithms. SIAM J. Comput. 18, pp. 594–607.
S. Rajasekaran and S. Sen. On parallel integer sorting. Acta Informatica 29, 1–15(1992).
R. Raman. The power of collision: randomized parallel algorithms for chaining and integer sorting. Proc. 10th Conf. on Foundations of Software Technology and Theoretical Computer Science, Springer Lecture Notes in Computer Science, Vol. 472, pp. 161–175.
L. Valiant. Parallelism in comparison problems. SIAM J. Comput., 4, pp. 348–355(1975).
R.A. Wagner and Y. Han. Parallel algorithms for bucket sorting and the data dependent prefix problem. Proc. 1986 International Conf. on Parallel Processing, pp. 924–930.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Han, Y., Shen, X. (1995). Conservative algorithms for parallel and sequential integer sorting. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030847
Download citation
DOI: https://doi.org/10.1007/BFb0030847
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60216-3
Online ISBN: 978-3-540-44733-7
eBook Packages: Springer Book Archive