Abstract
We present the first optimal parallel algorithms for the verification and sensitivity analysis of minimum spanning trees. Our algorithms are deterministic and run inO(logn) time and require linear-work in the CREW PRAM model. These algorithms are used as a subroutine in the linear-work randomized algorithm for finding minimum spanning trees of Cole, Klein, and Tarjan.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Alon and B. Schieber, Optimal Preprocessing for Answering On-Line Product Queries, Unpublished manuscript.
B. Awerbuch and Y. Shiloach, New Connectivity and MSF Algorithms for Shuffle-Exchange Network and PRAM,IEEE Trans. Comput. 36(10) (1987), 1258–1263.
H. Booth and J. Westbrook, Linear Algorithms for Analysis of Minimum Spanning and Shortest Path Trees in Planar Graphs, TR-768, Department of Computer Science, Yale University, Feb. 1990.
R. Cole, P. Klein, and R. E. Tarjan, A Linear-work Parallel Algorithm for Finding Minimum Spanning Trees,Proc. 6th ACM Symp. on Parallel Algorithms and Architectures, 1994.
B. Dixon, M. Rauch, and R. E. Tarjan, Verification and Sensitivity Analysis of Minimum Spanning Trees in Linear Time,SIAM J. Comput. 21(6) (1992), 1184–1192.
H. N. Gabow, Z. Galil, T. Spencer, and R. E. Tarjan, Efficient Algorithms for Finding Minimum Spanning Trees in Undirected and Directed Graphs,Combinatorica 6(2) (1986), 109–122.
D. Harel and R. E. Tarjan, Fast Algorithms for Finding Nearest Common Ancestors,SIAM J. Comput. 13(2) (1984), 338–355.
D. B. Johnson and P. Metaxas, A Parallel Algorithm for Computing Minimum Spanning Trees,Proc. 4th ACM Symp. on Parallel Algorithms and Architectures, 1992, pp. 363–372.
R. Karp and V. Ramachandran, Parallel Algorithms for Shared Memory Machines,Handbook of Theoretical Computer Science, Elsevier. Amsterdam, 1990, Chapter 17.
V. King, A Simpler Minimum Spanning Tree Verification Algorithm, Manuscript, 1994.
P. Klein and R. E. Tarjan, A Randomized Linear Time Algorithm for Finding Minimum Spanning Trees,Proc. 26th Annual ACM Symp. on Theory of Computing, 1994.
J. H. Reif, An Optimal Parallel Algorithm for Integer Sorting,Proc. 26th Annual ACM Symp. on Foundations of Computer Science, 1985, pp. 496–504.
R. E. Tarjan, Applications of Path Compressions on Balanced Trees,J. Assoc. Comput. Mach. 26(4) (1979), 690–715.
R. E. Tarjan, Sensitivity Analysis of Minimum Spanning Trees and Shortest Path Trees,Inform. Process. Lett. 14(1) (1982), 30–33. Corrigendum, ibid. Sensitivity Analysis of Minimum Spanning Trees and Shortest Path Trees,Inform. Process. Lett. 23 (1986), 219.
R. E. Tarjan,Data Structures and Network Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1983.
Author information
Authors and Affiliations
Additional information
Communicated by A. C.-C. Yao.
Research partially supported by a National Science Foundation Graduate Fellowship and by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center, Grant No. NSF-STC88-09648.
Research at Princeton University was partially supported by the National Science Foundation, Grant No. CCR-8920505, the Office of Naval Research, Contract No. N00014-91-J-1463, and by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center, Grant No. NSF-STC88-09648.
Rights and permissions
About this article
Cite this article
Dixon, B., Tarjan, R.E. Optimal parallel verification of minimum spanning trees in logarithmic time. Algorithmica 17, 11–18 (1997). https://doi.org/10.1007/BF02523235
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02523235