Abstract
For an undirected graph G, the node connectivity K is defined as the minimum number of nodes that must be removed to make the graph disconnected. The determination of K is a computationally demanding task for large graphs since even the most efficient algorithms require many evaluations of an expensive max flow function. Approximation methods for determining K replace the max flow function with a much faster algorithm that gives a lower bound on the number of node independent paths, but this frequently leads to an underestimate of K. We show here that with minor changes, the approximate method can be adapted to retain most of the performance benefits while still guaranteeing an accurate result.
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Acknowledgments
The author thanks Doug White for many useful discussions and for introducing him to the challenging problems in node connectivity and the identification of k-components in large graphs. Early stages of this work were supported in part by National Science Foundation grants OCI #0910847 Gordon: A Data Intensive Supercomputer and ACI#1053575 XSEDE: eXtreme Science and Engineering Discovery Environment (XSEDE) through the ECSS program.
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Sinkovits, R.S. (2021). Fast and Accurate Determination of Graph Node Connectivity Leveraging Approximate Methods. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12742. Springer, Cham. https://doi.org/10.1007/978-3-030-77961-0_41
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