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A parallel algorithm for finding a maximum flow in 0-1 networks

Published: 01 February 1987 Publication History
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    We present a parallel algorithm for finding the maximum flow in 0-1-networks. Our design is for a mesh-connected processor array and is based on the observation that an augmenting path in a 0-1-network can be found in time proportional to the number of vertices in the given network, rather than to the number of edges. Let integer n be the number of vertices in a 0-1-network. The time complexity of the parallel algorithm is Ο (n2+ε), where ε can be any small positive real number.

    References

    [1]
    Ford, L.R. Jr. and D.R. Fulkerson, Flows in Networks, Princeton University Press, 1962.
    [2]
    Dinic, E.A., Algorithm for Solution of a Problem of Maximum Flow in a Network with Power Estimation, Soviet Math. Dokl. 11, (1970), 1277-1280.
    [3]
    Even, S. and Tarjan, R.E., Network Flow and Testing Graph Connectivity, SIAM J. on Comput. 4, (1975), 507-518.
    [4]
    Jonson D.B. and S.M. Venkatesan, Parallel Algorithms for Minimum Cuts and Maximum Flows in Planar Networks, Proc. Twenty-third Annual IEEE Syrup. Foundations of Computer Science, 1983, 244-254.
    [5]
    Ullman, J.D., Computational Aspects of VLSI, Computer Science Press, 1984.
    [6]
    Atallah, M.J. and S.R. Kosaraju, Graph Problems on a Mesh-Connected Processor Army, Proc. 14th Annual ACM Symposium on the Theory of Computing, 1982, 345-353.
    [7]
    Guibas, L.J., H.T. Kung and C.D. Thompson, Direct VLSI Implementation. of Combinatorial Algorithms, Proc. Caltech Conf. on VLSI, 1979, 509-525.
    [8]
    Kung, H.T., The Structure of Parallel Algorithms, in Advances in Computers, vol. 19, M.C. Yovits (ed.), Academic Press, Inc., 1980, 65-112.
    [9]
    Berge, C., Graphs and Hypergraphs, North-Holland Publishing Company, Amsterdam, 1973.
    [10]
    Even, S., Graph Algorithms, Computer Science Press, Potomac, 1979.

    Cited By

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    • (2010)K-TreeComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2010.02.01354:11(1864-1884)Online publication date: 1-Aug-2010
    • (2008)Flow Maximization for NoC Routing AlgorithmsProceedings of the 2008 IEEE Computer Society Annual Symposium on VLSI10.1109/ISVLSI.2008.52(335-340)Online publication date: 7-Apr-2008

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    cover image ACM Conferences
    CSC '87: Proceedings of the 15th annual conference on Computer Science
    February 1987
    473 pages
    ISBN:0897912187
    DOI:10.1145/322917
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    New York, NY, United States

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    Published: 01 February 1987

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    • (2010)K-TreeComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2010.02.01354:11(1864-1884)Online publication date: 1-Aug-2010
    • (2008)Flow Maximization for NoC Routing AlgorithmsProceedings of the 2008 IEEE Computer Society Annual Symposium on VLSI10.1109/ISVLSI.2008.52(335-340)Online publication date: 7-Apr-2008

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