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A new graph triconnectivity algorithm and its parallelization

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Abstract

We present a new algorithm for finding the triconnected components of an undirected graph. The algorithm is based on a method of searching graphs called ‘open ear decomposition’. A parallel implementation of the algorithm on a CRCW PRAM runs inO(log2 n) parallel time usingO(n+m) processors, wheren is the number of vertices andm is the number of edges in the graph.

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References

  1. R. Cole: Parallel merge sort,SIAM J. Comput. 17 (1988), 770–785.

    Google Scholar 

  2. R. Cole, U. Vishkin: Approximate and exact parallel scheduling with applications to list, tree and graph problems,Proc. 27th Ann. IEEE Symp. on Foundations of Comp. Sci. 1986, 478–491.

  3. S. Even:Graph Algorithms, Computer Science Press, Rockville, MD, 1979.

    Google Scholar 

  4. J. E. Hopcroft, R. E. Tarjan: Dividing a graph into triconnected components,SIAM J. Comput. 2 (1973), 135–158.

    Google Scholar 

  5. J. E. Hopcroft, R. E. Tarjan: Finding the triconnected components of a graph, TR 72-140, Computer Science Department, Cornell University, Ithaca, NY, 1972.

    Google Scholar 

  6. J. Ja'Ja, J. Simon: Parallel algorithms in graph theory: planarity testing,SIAM J. Comput. 11 (1982), 314–328.

    Google Scholar 

  7. A. Kanevsky, V. Ramachandran: Improved algorithms for graph four-connectivity,Jour. Comput. Syst. Sci. 42 (1991), 288–306.

    Google Scholar 

  8. R. M. Karp, V. Ramachandran: Parallel algorithms for shared memory machines,Handbook of Theoretical Computer Science, J. Van Leeuwen, ed., North Holland, 1990, 869–941.

  9. L. Lovász: Computing ears and branchings in parallel,Proc. 26th IEEE Ann. Symp. on Foundations of Comp. Sci. 1985, 464–467.

  10. Y. Maon, B. Schieber, U. Vishkin: Parallel ear decomposition search (EDS) and st-numbering in graphs,Theoretical Comput. Sci. 47 (1986), 277–298.

    Google Scholar 

  11. G. L. Miller, V. Ramachandran: Efficient parallel ear decomposition with applications, unpublished manuscript, MSRI, Berkeley, CA, January 1986.

    Google Scholar 

  12. G. L. Miller, V. Ramachandran: A new graph triconnectivity algorithm and its parallelization,Proc. 19th Annual ACM Symp. on Theory of Computing, 1987, 254–263.

  13. G. L. Miller, J. H. Reif: Parallel tree contraction and its applications,Proc. 26th IEEE Symp. on Foundations of Comp. Sci., 1985, 478–489.

  14. V. Ramachandran, U. Vishkin: Efficient parallel triconnectivity in logarithmic time,VLSI Algorithms and Architectures, Springer Verlag LNCS319 (1988), 33–42.

    Google Scholar 

  15. R. E. Tarjan, U. Vishkin: Finding biconnected components and computing tree functions in logarithmic parallel time,SIAM J. Comput. 14 (1985), 862–874.

    Google Scholar 

  16. W. T. Tutte:Connectivity in Graphs, University of Toronto Press, 1966.

  17. H. Whitney: Non-separable and planar graphs,Trans. Amer. Math. Soc. 34 (1932), 339–362.

    Google Scholar 

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Supported by NSF Grant DCR 8514961.

Supported by NSF Grant ECS 8404866 and the Semiconductor Research Corporation Grant 86-12-109.

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Miller, G.L., Ramachandran, V. A new graph triconnectivity algorithm and its parallelization. Combinatorica 12, 53–76 (1992). https://doi.org/10.1007/BF01191205

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  • DOI: https://doi.org/10.1007/BF01191205

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