Abstract
New features of our DSC system for distributing a symbolic computation task over a network of processors are described. A new scheduler sends parallel subtasks to those compute nodes that are best suited in handling the added load of CPU usage and memory. Furthermore, a subtask can communicate back to the process that spawned it by a co-routine style calling mechanism. Two large experiments are described in this improved setting. We have implemented an algorithm that can prove a number of more than 1,000 decimal digits prime in about 2 months elapsed time on some 20 computers. A parallel version of a sparse linear system solver is used to compute the solution of sparse linear systems over finite fields. We are able to find the solution of a 100,000 by 100,000 linear system with about 10.3 million non-zero entries over the Galois field with 2 elements using 3 computers in about 54 hours CPU time.
This material is based on work supported in part by the National Science Foundation under Grant No. CCR-90-06077, CDA-91-21465, and under Grant No. CDA-88-05910.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Literature cited
Batut, C., Bernardi, D., Cohen, H., and Olivier, M., “User's Guide to PARI-GP,” Manual, February 1991.
Bitmead, R. R. and Anderson, B. D. O., “Asymtotically fast solution of Toeplitz and related systems of linear equations,” Linear Algebra Applic. 34, pp. 103–116 (1980).
Char, B. W., “Progress report on a system for general-purpose parallel symbolic algebraic computation,” in Proc. 1990 Internat. Symp. Symbolic Algebraic Comput., edited by S. Watanabe and M. Nagata; ACM Press, pp. 96–103, 1990.
Collins, G. E., Johnson, J. R., and Küchlin, W., “PARSAC-2: A multi-threaded system for symbolic and algebraic computation,” Tech. Report TR.38, Comput. and Information Sci. Research Center, Ohio State University, December 1990.
Coppersmith, D., “Solving linear equations over GF(2) via block Wiedemann algorithm,” Math. Comput., p. to appear (1992).
Diaz, A., “DSC,” Users Manual (2nd ed.), Dept. Comput. Sci., Rensselaer Polytech. Inst., Troy, New York, 1992.
Diaz, A., Kaltofen, E., Schmitz, K., and Valente, T., “DSC A System for Distributed Symbolic Computation,” in Proc. 1991 Internat. Symp. Symbolic Algebraic Comput., edited by S. M. Watt; ACM Press, pp. 323–332, 1991.
Gohberg, I., Kailath, T., and Koltracht, I., “Efficient solution of linear systems of equations with recursive structure,” Linear Algebra Applic. 80, pp. 81–113 (1986).
Hong, H. and Schreiner, W., “Programming in PACLIB,” SIGSAM Bull. 26/4, pp. 1–6 (1992).
Kaltofen, E., “Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems,” in Proc. AAECC-10, Springer Lect. Notes Comput. Sci. 673, edited by G. Cohen, T. Mora, and O. Moreno; pp. 195–212, 1993.
Kaltofen, E. and Trager, B., “Computing with polynomials given by black boxes for their evaluations: Greatest common divisors, factorization, separation of numerators and denominators,” J. Symbolic Comput. 9/3, pp. 301–320 (1990).
Kaltofen, E., Valente, T., and Yui, N., “An improved Las Vegas primality test,” Proc. ACM-SIGSAM 1989 Internat. Symp. Symbolic Algebraic Comput., pp. 26–33 (1989).
Kogge, P. M., The Architecture of Symbolic Computers; McGraw-Hill, Inc., New York, N.Y., 1991.
Morain, F., “Distributed primality proving and the primality of (23539+1)/3,” in Advances in Cryptology—EUROCRYPT '90, Springer Lect. Notes Comput. Sci. 473, edited by I. B. Damgård; pp. 110–123, 1991.
Morf, M., “Doubling algorithms for Toeplitz and related equations,” in Proc. 1980 IEEE Internat. Conf. Acoust. Speech Signal Process.; IEEE, pp. 954–959, 1980.
Seitz, S., “Algebraic computing on a local net,” in Computer Algebra and Parallelism, Springer Lect. Notes Math. 584; Springer Verlag, New York, N. Y., pp. 19–31, 1992.
Valente, T., “A distributed approach to proving large numbers prime,” Ph.D. Thesis, Dept. Comput. Sci., Rensselaer Polytech. Instit., Troy, New York, December 1992.
Wiedemann, D., “Solving sparse linear equations over finite fields,” IEEE Trans. Inf. Theory IT-32, pp. 54–62 (1986).
Author information
Authors and Affiliations
Corresponding author
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Diaz, A., Hitz, M., Kaltofen, E., Lobo, A., Valente, T. (1993). Process scheduling in DSC and the large sparse linear systems challenge. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1993. Lecture Notes in Computer Science, vol 722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013169
Download citation
DOI: https://doi.org/10.1007/BFb0013169
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57235-0
Online ISBN: 978-3-540-47985-7
eBook Packages: Springer Book Archive