Abstract
Until recently, a large majority of theoretical work in parallel algorithms has ignored communication costs and other realities of parallel computing. This paper attempts to address this issue by developing parallel algorithms that not only are efficient using standard theoretical analysis techniques, but also require a minimal amount of communication. The specific parallel algorithms developed here include one to find the set of maximal cliques and one to find a perfect elimination ordering of a choral graph.
Extended Abstract
Portions of this research were performed at the Mathematical Sciences Section of Oak Ridge National Laboratory and partially supported by the Applied Mathematics Science Research Program, Office of Energy Research, U.S. Department of Energy under contract DE-AC05-840R21400 with Martin Marietta Energy Systems Inc.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
C. Beeri, R. Fagin, D. Maier and M. Yannakakis, “On the desirability of acyclic database schemes,” Journal of the Association for Computing Machinery vol. 30, no. 3, pp. 205–212, 1974.
M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, London, 1980.
C. Ho and R. C. T. Lee, “Efficient parallel algorithms for finding maximal cliques, clique trees, and minimum coloring on chordal graphs,” Information Processing Letters Vol. 28, pp. 301–309, 1988.
C. Ho and R. C. Lee, “Counting clique trees and perfect elimination schemes in parallel,” Information Processing Letters Vol. 31, pp. 61–68, 1989.
P. N. Klein, “Efficient parallel algorithms for chordal graphs,” Symposium on Foundations of Computer Science, pp. 150–161, October 1988.
J. Naor, M. Naor, A. A. Schaffer, “Fast parallel algorithms for chordal graphs,” Proceedings 19th Annual ACM Symposium on Theory of Computing, pp. 355–364, 1987.
C. Papadimitriou and M. Yannakakis “Towards an Architecture Independent Analysis of Parallel Algorithms,” SIAM Journal of Computing Vol. 19, pp. 322–328, April 1990.
D. J. Rose, “Triangulated Graphs and the Elimination Process,” Journal of Mathematical Analysis and Applications, Vol. 32, pp. 597–609, 1970.
D. J. Rose, “A graph-theoretic study of the numerical solution of sparse positive definite systems of linear equations,” in Graph Theory and Computing, ed. R. Read, pp. 183–217, Academic Press, New York, 1973.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kirsch, E.S., Blair, J.R.S. (1991). Practical parallel algorithms for chordal graphs. In: Dehne, F., Fiala, F., Koczkodaj, W.W. (eds) Advances in Computing and Information — ICCI '91. ICCI 1991. Lecture Notes in Computer Science, vol 497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54029-6_185
Download citation
DOI: https://doi.org/10.1007/3-540-54029-6_185
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54029-8
Online ISBN: 978-3-540-47359-6
eBook Packages: Springer Book Archive