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On the Algebraic Theory of Loop Free Routing

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Distributed Computer and Communication Networks (DCCN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 12563))

Abstract

Validation models not only provide a better understanding of the system, but can also help in improving the reliability and robustness of the design. EIGRP metric can be modeled algebraically using bi-semigroups and semirings in case the cost function is homomorphic [1]. EIGRP uses DUAL algorithm which is the basis for loop-free distance vector routing with non lexical metric. DUAL was validated using the classical shortest path problem [13, 20]. However, it was shown that DUAL does not perform as expected in the absence of monotonicity [1, 23]. This article approaches loop free routing from an algebraic perspective. Conditions for loop free routing and the relations between them were presented algebraically and proved correct. Then, we investigate loop free routing in the presence and the absence of monotonicity. Our goal is to provide theory for loop free routing with an arbitrary metric.

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References

  1. Khayou, H., Sarakbi, B.: A validation model for non-lexical routing protocols. J. Netw. Comput. Appl. 98, 58–64 (2017)

    Article  Google Scholar 

  2. Sobrinho, J.L.: An algebraic theory of dynamic network routing. IEEE/ACM Trans. Netw. 13(5), 1160–1173 (2005)

    Article  Google Scholar 

  3. Albrightson, R., Garcia-Luna-Aceves, J.J., Boyle, J.: EIGRP- a fast routing protocol based on distance vectors. Proc. Networld/Interop 94 (1994)

    Google Scholar 

  4. Sobrinho, J.L.: Algebra and algorithms for QoS path computation and hop-by-hop routing in the Internet. IEEE/ACM Trans. Netw. 10(4), 541–550 (2002)

    Article  Google Scholar 

  5. Sobrinho, J.L.: Network routing with path vector protocols: theory and applications. In: Proceedings of the 2003 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (2003)

    Google Scholar 

  6. Gurney, A.J.T.: Construction and verification of routing algebras. Diss. University of Cambridge (2010)

    Google Scholar 

  7. Sobrinho, J.L., Griffin, T.G.: Routing in equilibrium. Math. Theory Netw. Syst. (2010)

    Google Scholar 

  8. Griffin, T.G., Sobrinho, J.L.: Metarouting. In: Proceedings of the 2005 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (2005)

    Google Scholar 

  9. Gondran, M., Minoux, M.: Graphs, Dioids and Semirings: New Models and Algorithms, vol. 41. Springer, New York (2008). https://doi.org/10.1007/978-0-387-75450-5

    Book  MATH  Google Scholar 

  10. Baras, J.S., Theodorakopoulos, G.: Path problems in networks. Synth. Lect. Commun. Netw. 3(1), 1–77 (2010)

    Article  Google Scholar 

  11. Griffin, T.G., Gurney, A.J.T.: Increasing bisemigroups and algebraic routing. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS 2008. LNCS, vol. 4988, pp. 123–137. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78913-0_11

    Chapter  Google Scholar 

  12. Dijkstra, E.W., Scholten, C.S.: Termination detection for diffusing computations. Inf. Process. Lett. 11(1), 1–4 (1980)

    Article  MathSciNet  Google Scholar 

  13. Garcia-Luna-Aceves, J.J.: A unified approach to loop-free routing using distance vectors or link states. ACM SIGCOMM Comput. Commun. Rev. 19(4), 212–223 (1989)

    Article  Google Scholar 

  14. Jaffe, J., Moss, F.: A responsive distributed routing algorithm for computer networks. IEEE Trans. Commun. 30(7), 1758–1762 (1982)

    Article  Google Scholar 

  15. Dynerowicz, S., Griffin, T.G.: On the forwarding paths produced by internet routing algorithms. In: 2013 21st IEEE International Conference on Network Protocols (ICNP). IEEE (2013)

    Google Scholar 

  16. Mohri, M.: Semiring frameworks and algorithms for shortest-distance problems. J. Autom. Lang. Comb. 7(3), 321–350 (2002)

    MathSciNet  MATH  Google Scholar 

  17. Alim, M.A., Griffin, T.G.: On the interaction of multiple routing algorithms. In: Proceedings of the Seventh COnference on Emerging Networking EXperiments and Technologies (2011)

    Google Scholar 

  18. Malkin, G.: RFC 2453: RIP Version 2 (1998)

    Google Scholar 

  19. Rekhter, Y., Li, T., Hares, S.: RFC 4271: A Border Gateway Protocol 4 (BGP-4) (2006)

    Google Scholar 

  20. Garcia-Lunes-Aceves, J.J.: Loop-free routing using diffusing computations. IEEE/ACM Trans. Netw. 1(1), 130–141 (1993)

    Article  Google Scholar 

  21. Griffin, T.: An Algebraic approach to internet routing. University of Cambridge. Lecture Notes (2010)

    Google Scholar 

  22. Savage, D., et al.: RFC 7868: Cisco’s Enhanced Interior Gateway Routing Protocol (EIGRP) (2016)

    Google Scholar 

  23. Gouda, M.G., Schneider, M.: Maximizable routing metrics. IEEE/ACM Trans. Netw. 11(4), 663–675 (2003). https://doi.org/10.1109/TNET.2003.815294

    Article  Google Scholar 

  24. Sobrinho, J.L.: Correctness of routing vector protocols as a property of network cycles. IEEE/ACM Trans. Netw. 25(1), 150–163 (2017). https://doi.org/10.1109/TNET.2016.2567600

    Article  Google Scholar 

  25. Saad, M.: Non-isotonic routing metrics solvable to optimality via shortest path. J. Comput. Netw. 145, 89–95 (2018)

    Article  Google Scholar 

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute”, Krasnokazarmennaya 14, 111250, Moscow, Russia

    Hussein Khayou, Margarita A. Rudenkova & Leonid I. Abrosimov

Authors
  1. Hussein Khayou
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  2. Margarita A. Rudenkova
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  3. Leonid I. Abrosimov
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Corresponding authors

Correspondence to Hussein Khayou , Margarita A. Rudenkova or Leonid I. Abrosimov .

Editor information

Editors and Affiliations

  1. Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Khayou, H., Rudenkova, M.A., Abrosimov, L.I. (2020). On the Algebraic Theory of Loop Free Routing. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks. DCCN 2020. Lecture Notes in Computer Science(), vol 12563. Springer, Cham. https://doi.org/10.1007/978-3-030-66471-8_14

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  • DOI: https://doi.org/10.1007/978-3-030-66471-8_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-66470-1

  • Online ISBN: 978-3-030-66471-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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