Abstract
Randomization offers elegant solutions to some problems in parallel computing. In addition to improved efficiency it often leads to simpler and practical algorithms. In this paper we discuss some of the characteristics of randomized algorithms and also give applications in computational geometry where use of randomization gives us significant advantage over the best known deterministic parallel algorithms.
Supported in part by Air Force Contract AFSOR-87-0386, ONR contract N00014-87-K-0310, NSF grant CCR-8696134, DARPA/ARO contract DAAL03-88-K-0185, DARPA/ISTO contract N00014-88-K-0458.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Bibliography
L. Adleman and K. Manders, ‘Reducibility, Randomness and Untractability," Proc. 9th ACM STOC, 1977, pp. 151–163.
A. Aggarwal and R. Anderson, "A Random NC Algorithm for Depth First Search," Proc of the 19th ACM STOC, 1987, pp. 325–334.
Aggarwal et al., ‘Parallel Computational Geometry,’ Proc. of the 26th Annual Symp on F.O.C.S., 1985, pp. 468–477. Also appears in ALGORITHMICA, Vol. 3, No. 3, 1988, pp. 293–327.
Atallah, Cole and Goodrich, ‘Cascading Divide-and-conquer: A technique for designing parallel algorithms, Proc. of the 28th Annual Symp. on F.O.C.S., 1987, pp. 151–160.
Clarkson, ‘Applications of random sampling in Computational Geometry II,’ Proc. of the 4th Annual Symp. on Computational Geometry, June 1988, pp. 1–11.
N. Dadoun and D. Kirkpatrick, ‘Parallel Processing for efficient subdivision search,’ Proc. of the 3rd Annual Symp. on Computational Geometry, pp. 205–214, 1987.
H. Gazit, ‘An optimal randomized parallel algorithm for finding connected components in a graph,’ Proc of the IEEE FOCS, 1986, pp. 492–501.
C.A.R. Hoare, ‘Quicksort,’ Computer Journal, 5(1), 1962, pp.10–15.
H. Karloff and P. Raghavan, ‘Randomized algorithms and Pseudorandom number generation,’ Proc. of the 20th Annual STOC, 1988.
G. Miller and J.H. Reif, ‘Parallel Tree contraction and its applications,’ Proc of the IEEE FOCS, 1985, pp. 478–489.
M.O. Rabin, ‘Probabilistic Algorithms,’ in: J.F. Traub, ed., Algorithms and Complexity, Academic Press, 1976, pp. 21–36.
S. Rajasekaran, ‘Randomized Parallel Computation,’ Ph.D. Thesis, Aiken Computing Lab, Harvard University, 1988.
J.H. Reif, ‘On synchronous parallel computations with independent probabilistic choice,’ SIAM J. Comput., Vol. 13, No. 1, Feb 1984, pp. 46–56.
Reif and Sen, ‘Optimal randomized parallel algorithms for computational geometry,’ Proc. of the 16th Intl. Conf. on Parallel Processing, Aug 1987. Revised version available as Tech Rept CS-88-01, Computer Science Dept, Duke University.
J. Reif and S. Sen, ‘Polling: A new random sampling technique for Computational Geometry,’ Proc. of the 21st STOC, 1989.
J.H. Reif and L. Valiant, ‘A Logarithmic Time Sort for Linear Size networks,’ J. of ACM, Vol. 34, No.1, Jan '87, pp. 60–76.
R. Solovay and V. Strassen, ‘A fast Monte-Carlo test for primality,’ SIAM Journal of Computing, 1977, pp. 84–85.
L.G. Valiant, ‘A scheme for fast parallel communication,’ SIAM Journal of Computing, vol. 11, no. 2, 1982, pp. 350–361.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Reif, J.H., Sen, S. (1989). Randomization in parallel algorithms and its impact on computational geometry. In: Djidjev, H. (eds) Optimal Algorithms. OA 1989. Lecture Notes in Computer Science, vol 401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51859-2_1
Download citation
DOI: https://doi.org/10.1007/3-540-51859-2_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51859-4
Online ISBN: 978-3-540-46831-8
eBook Packages: Springer Book Archive