Abstract
We present an efficient technique for parallel manipulation of data structures that avoids memory access conflicts. That is, this technique works on the Exclusive Read/Exclusive Write (EREW) model of computation, which is the weakest shared memory, MIMD machine model. It is used in a new parallel radix sort algorithm that is optimal for keys whose values are over a small range. Using the radix sort and known results for parallel prefix on linked lists, we develop parallel algorithms that efficiently solve various computations on trees and “unicycular graphs.” Finally, we develop parallel algorithms for connected components, spanning trees, minimum spanning trees, and other graph problems. All of the graph algorithms achieve linear speedup for all but the sparsest graphs.
Similar content being viewed by others
References
A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass., 1974.
M. J. Atallah and S. E. Hambrusch, Solving Tree Problems on a Mesh-Connected Processor Array,Proc. 26th Annual Symposium on Foundations of Computer Science, Oct. 1985, 222–231.
D. Cheriton and R. E. Tarjan, Finding Minimum Spanning Trees,SIAM J. Comput., 1976, 724–742.
R. Cole and U. Vishkin, Deterministic Coin Tossing and Accelerating Cascades: Micro and Macro Techniques for Designing Parallel Algorithms,Proc. 18th Annual ACM Symposium on Theory of Computation, 1986, 206–219.
R. Cole and U. Vishkin, Approximate and Exact Parallel Scheduling with Applications to List, Tree and Graph Problems,Proc. 27th Annual Symposium on Foundations of Computer Science, 1986, 478–491.
R. Cole and U. Vishkin, The Accelerated Centroid Decomposition Technique for Optimal Parallel Tree Evaluation in Logarithm Time, Submitted for Publication.
D. M. Eckstein, Parallel Processing Using Depth-First and Breadth-First Search, Ph.D. Thesis, University of Iowa, July 1977.
D. E. Knuth,The Art of Computer Programming, Vol. 1, Addison-Wesley, Reading, Mass., 1973.
C. P. Kruskal, L. Rudolph, and M. Snir, The Power of Parallel Prefix,IEEE Trans. Comput.,34, 1985, 965–968.
S. C. Kwan and W. L. Ruzzo, Adaptive Parallel Algorithms for Finding Minimum Spanning Trees,Proc. 1984 International Conference on Parallel Processing, Aug. 1984, 439–443.
R. Ladner and M. Fischer, Parallel Prefix Computation,J. Assoc. Comput. Mach., 1980, 831–838.
G. Miller and J. Reif, Parallel Tree Contraction and Its Application,Proc. 26th Annual Symposium on Foundations of Computer Science, 1985, 496–503.
J. T. Schwartz, Ultracomputers,ACM Trans. Program. Lang. Systems, 1980, 484–521.
M. Snir, On Parallel Searching,Proc. ACM Symposium on Distributed Computing, Aug. 1982, 242–253.
Q. F. Stout, Tree-Based Graph Algorithms for Some Parallel Computers,Proc. 1985 International Conference on Parallel Processing, Aug. 1985, 727–731.
R. E. Tarjan and U. Vishkin, Finding Biconnected Components and Computing Tree Functions in Logarithmic Time,Proc. 25th Annual Symposium on Foundations of Computer Science, Oct. 1984, 12–20.
U. Vishkin, Randomized Speedups in Parallel Computations,Proc. 16th Annual ACM Symposium on Theory of Computing, April 1984, 230–239.
J. C. Wyllie, The Complexity of Parallel Computations, Ph.D. Dissertation, Department of Computer Science, Cornell University, Ithaca, N.Y., 1979.
Author information
Authors and Affiliations
Additional information
Communicated by F. Thomson Leighton.
Part of this work was done while the first author was at the University of Illinois, Urbana-Champaign, the second author was at Carnegie-Mellon University, and the third author was at the Hebrew University and the Courant Institute of Mathematical Sciences, New York University. A preliminary version of this work was presented at the 1986 International Conference on Parallel Processing.
Rights and permissions
About this article
Cite this article
Kruskal, C.P., Rudolph, L. & Snir, M. Efficient parallel algorithms for graph problems. Algorithmica 5, 43–64 (1990). https://doi.org/10.1007/BF01840376
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01840376