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Parallel algorithm to find maximum capacity paths

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Cybernetics and Systems Analysis Aims and scope

Conclusion

An important advantage of the proposed algorithm compared with previous algorithms is that it easily finds the maximum flow between a given pair of network nodess, t. This requires onlym repetitions of the algorithm, wherem is the number of edges in the graphG defining the given network. The time complexity of finding the maximum flow by the proposed algorithm thus does not exceed O(mn). The procedure to find the maximum flow consists of two steps.

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References

  1. N. Christofides, Graph Theory: An Algorithmic Approach, Academic Press, New York (1975).

    MATH  Google Scholar 

  2. G. Frank and I. Frisch, Networks, Communication, and Flows [Russian translation], Svyaz', Moscow (1978).

    Google Scholar 

  3. S. I. Baranov and V. A. Sklyarov, Programmable LSI Digital Devices with Array Structure [in Russian], Radio i Svyaz', Moscow (1986).

    Google Scholar 

  4. S. V. Listrovoi, “Parallel algorithm for the shortest path problem in a graph,” Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 4, 184–195 (1990).

  5. S. V. Listrovoi, “Architecture of cyclic parallel computing systems,” Elektron. Model.,14, No. 2, 28–36 (1992).

    Google Scholar 

  6. S. V. Listrovoi, “A device for solving problems in graphs,” USSR Author's Certificate 4,784,401; Class 606 F15/20, Otkrytiya, Izobreteniya, No. 20, 135 (1992).

  7. J. Edmonds and R. M. Karp, “Theoretical improvements in algorithmic efficiency for network flow problems,” J. ACM,19 [sic].

  8. E. A. Dinits, “Algorithm to solve the maximum network flow problem in exponential time,” Dokl. Akad. Nauk SSSR,194, No. 4, 754–757 (1970).

    MathSciNet  Google Scholar 

  9. A. V. Karzanov, “Finding the maximum network flow by preflow method,” Dokl. Akad. Nauk SSSR,215, No. 1, 49–52 (1974).

    MathSciNet  Google Scholar 

  10. B. V. Cherkasskii, “Algorithm to construct maximum network flow in time O(¦V¦2 √¦E¦,” Mat. Metod. Resh. Ekon. Zad.,6, 117–126 (1977).

    Google Scholar 

  11. Z. Calil, “A new algorithm for the maximum flow problem,” Proc. 19th Symp. on Foundations of Computer Science, IEEE, New York (1978), pp. 231–245.

  12. Z. Calil and A. Naamad, “Network flow and generalized path compression,” Proc. 11th Annual ACM Symp. on the Theory of Computing, May 1979, ACM, New York (1979), pp. 13–26.

    Google Scholar 

  13. Z. Calil and A. Naamad, “An O(EVlog V) algorithm for the maximal flow problem,” J. Comput. Syst. Sci.,21, No. 2, 217 (1980).

    Google Scholar 

  14. S. Even and R. E. Tarjan, “Network flow and testing graph connectivity,” SIAM Comput.,4, No. 4, 507–518 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  15. B. V. Cherkasskii, “A fast maximum network flow algorithm,” Sb. Trudov VNIISI, pp. 90–96 (1979).

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Authors
  1. S. V. Listrovoi
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  2. V. I. Khrin
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Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 125–134, March–April, 1998.

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Listrovoi, S.V., Khrin, V.I. Parallel algorithm to find maximum capacity paths. Cybern Syst Anal 34, 261–268 (1998). https://doi.org/10.1007/BF02742076

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