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Perfect Sets of Paths in the Full Graph of SDN Switches

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Abstract

This paper investigates the implementation of virtual networks on the SDN data plane modeled by a graph of physical connections between network nodes. A virtual network is defined as a set of ordered host pairs (sender and receiver) and is implemented by a set of host–host paths that uniquely determine the settings of switches. A set of paths is said to be perfect if any subset of its paths can be implemented loop-free, i.e., without endless movement of packets in a loop, without duplicate paths (when the host receives the same packet several times), and without unintended paths (when the host receives a packet directed to some other host). In the case where the switchgraph is a complete graph, sufficient conditions for the existence of the largest perfect set of paths connecting all pairs of different hosts are established. Algorithms for constructing this largest perfect set are proposed and their complexity is estimated. The paper also reports preliminary results of conducted computer experiments, which suggest that the proposed sufficient conditions are not necessary ones.

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Notes

  1. In this paper, we consider packets for a single flow (a flow with one identifier); therefore, when describing rules and paths, the parameter vector σ is omitted.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 20-07-00338-a.

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Authors and Affiliations

  1. Ivannikov Institute for System Programming, Russian Academy of Sciences, ul. Solzhenitsyna 25, 109004, Moscow, Russia

    I. B. Burdonov, N. V. Yevtushenko & A. S. Kossatchev

  2. Moscow State University, 119234, Moscow, Russia

    E. M. Vinarskii

  3. National Research University Higher School of Economics, ul. Myasnitskaya 20, 101000, Moscow, Russia

    N. V. Yevtushenko

Authors
  1. I. B. Burdonov
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  2. E. M. Vinarskii
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  3. N. V. Yevtushenko
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  4. A. S. Kossatchev
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Corresponding authors

Correspondence to I. B. Burdonov, E. M. Vinarskii, N. V. Yevtushenko or A. S. Kossatchev.

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Translated by Yu. Kornienko

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Burdonov, I.B., Vinarskii, E.M., Yevtushenko, N.V. et al. Perfect Sets of Paths in the Full Graph of SDN Switches. Program Comput Soft 47, 505–514 (2021). https://doi.org/10.1134/S0361768821070033

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  • DOI: https://doi.org/10.1134/S0361768821070033

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