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Strength and reinforcement of a network and tree packing

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Cybernetics and Systems Analysis Aims and scope

Abstract

We propose strictly polynomial-time algorithms for a number of network problems: (a) strength and reinforcement of a network. (b) attack and density of a network. (c) packing, covering, and partitioning of a network into spanning trees. The proposed algorithms are either new or have lower complexity than previously published algorithms.

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Literature Cited

  1. W. H. Cunningham, “Optimal attack and reinforcement of a network,” J. ACM,32, 549–561 (1985).

    Google Scholar 

  2. D. Gusfeld, “Connectivity and edge disjoint spanning trees,” Inform. Proc. Lett.,16, 87–89 (1983).

    Google Scholar 

  3. J. Edmonds, “Min partition of a matroid into independent subsets,” J. Res. Nat. Bureau Stand.,B 69, 65–72 (1965).

    Google Scholar 

  4. G. M. Adel'son-Vel'skii, E. A. Dinits, and A. V. Karzanov, Flow Algorithms [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  5. A. V. Goldberg and R. E. Tarjan, “A new approach to the maximum flow problem,” J. ACM,35, 921–940 (1988).

    Google Scholar 

  6. S. Toida, “Decomposition of a graph into dense subgraphs,” IEEE Trans. Circuits Syst.,32, 583–589 (1985).

    Google Scholar 

  7. J.-C. Picard and M. Queranne, “Selected applications of minimum cuts in networks,” INFOR. J.,20, 394–422 (1982).

    Google Scholar 

  8. W. H. Cunningham, “Minimum cuts, modular functions and matroid polyhedra,” Networks,15, 205–215 (1985).

    Google Scholar 

  9. V. A. Trubin, “Determining the strength of a graph,” Dokl. Akad. Nauk SSSR,316, 1065–1069 (1991).

    Google Scholar 

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Translated from Kibernetika, No. 2, pp. 67–75, March–April, 1991.

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Trubin, V.A. Strength and reinforcement of a network and tree packing. Cybern Syst Anal 27, 246–257 (1991). https://doi.org/10.1007/BF01068376

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  • DOI: https://doi.org/10.1007/BF01068376

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