Abstract
A new parallel algorithm for updating the minimum spanning tree of an n-vertex graph following the addition of a new vertex is presented. The algorithm runs in O(log n) time, using O(n) processors on a concurrent-read-exclusive-write parallel random access machine. The algorithm uses a divide-and-conquer strategy, and is superior to known results on this model, that either obtain O(log n) time performance using O(n2) processors, or employ O(n) processors but have a time complexity of O (log2 n).
This research was supported in part by an IBM Faculty Development Award.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Spira, P. and Pan, A., "On Finding and Updating Spanning Trees and Shortest Paths", SIAM J. Comp., 4 (1975), pp. 375–380.
Chin, F. and Houck, D., "Algorithms for Updating Minimum Spanning Trees", J. Comput. System Sci., 16 (1978), pp. 333–344.
Pawagi, S. and Ramakrishnan I. V., "Parallel Update of Graph Properties in Logarithmic Time", Proc. 1985 Intl. Conf. on Parallel Processing, (1985), pp. 186–193.
Tsin, Y. and Chin, F., "Efficient Parallel Algorithms for a Class of Graph Theoretic Algorithms", SIAM J. Comp., 14, (1984), pp. 580–599.
Savage, C. and Ja'Ja, J., "Fast Efficient Parallel Algorithms for some Graph Problems", SIAM J. Comp., 10, (1981), pp. 682–691.
Kwan, S. C., and Ruzzo, W. L., "Adaptive Parallel Algorithms for Finding Minimum Spanning Trees", Proc. of the 1984 Intl. Conf. on Parallel Processing, (1984), pp. 175–179.
Awerbuck, B. and Shiloach, Y., "New Connectivity and MSF Algorithms for UltraComputer And PRAM," Proc. of the 1983 Intl. Conf. on Parallel Processing, (1983), pp. 175–179.
Tarjan, R. E. and Vishkin, U., "Finding Biconnected Components and Computing Tree Functions in Logarithmic Time", 25th Annual ACM Symp. on Theory of Computing, (1984), pp. 230–239.
Lipton, R. J. and Tarjan, R. E., "A Separator Theorem for Planar Graphs", SIAM J. Appl. Math., Vol. 3, No. 2, (1979). pp. 177–189.
Vishkin, U., "An Efficient Parallel Strong Orientation", TR 109, Computer Science Department, New York University, New York, (1984).
Doshi, K. A. and Varman, P. J., "A Parallel Algorithm for Vertex Update of Minimum Spanning Trees," Technical Report, Department of Electrical and Computer Engineering, Rice University, Houston, (1986).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Varman, P., Doshi, K. (1986). A parallel vertex insertion algorithm for minimum spanning trees. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_92
Download citation
DOI: https://doi.org/10.1007/3-540-16761-7_92
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16761-7
Online ISBN: 978-3-540-39859-2
eBook Packages: Springer Book Archive