# A parallel vertex insertion algorithm for minimum spanning trees

Conference paper

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## 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(n^{2}) processors, or employ O(n) processors but have a time complexity of O (log^{2} n).

## Keywords

Minimum Span Tree Euler Number Algorithm SplitTree Tree Edge Special Vertex
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## References

- 1.Spira, P. and Pan, A., "On Finding and Updating Spanning Trees and Shortest Paths",
*SIAM J. Comp.*,**4**(1975), pp. 375–380.Google Scholar - 2.Chin, F. and Houck, D., "Algorithms for Updating Minimum Spanning Trees",
*J. Comput. System Sci.*,**16**(1978), pp. 333–344.Google Scholar - 3.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.Google Scholar - 4.Tsin, Y. and Chin, F., "Efficient Parallel Algorithms for a Class of Graph Theoretic Algorithms",
*SIAM J. Comp.*,**14**, (1984), pp. 580–599.Google Scholar - 5.Savage, C. and Ja'Ja, J., "Fast Efficient Parallel Algorithms for some Graph Problems",
*SIAM J. Comp.*,**10**, (1981), pp. 682–691.Google Scholar - 6.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.Google Scholar - 7.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.Google Scholar - 8.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.Google Scholar - 9.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.Google Scholar - 10.Vishkin, U., "An Efficient Parallel Strong Orientation", TR 109, Computer Science Department, New York University, New York, (1984).Google Scholar
- 11.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).Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1986