Skip to main content
SpringerLink
Log in

Exploring the stratified shortest-paths problem

  • Research Article
  • Published:
Networking Science

Abstract

In the last ten years it has become clear that some Internet routing protocols do not compute globally optimal paths, but only locally optimal ones. This represents something rather novel in the context of the vast literature on routing protocols for data networking. This paper uses the stratified shortest-paths problem (SSPP) as a tool for exploring the borderline between local and global optimality problems. The SSPP can help us understand inter-domain routing with BGP, or aid in the design of new policy-rich intra-domain protocols. The paper contains a tutorial overview of the algebraic concepts used.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. S. Baras and G. Theodorakopoulos, Path Problems in Networks. San Rafael, USA: Morgan & Claypool, 2010.

    Google Scholar 

  2. B. Carré, Graphs and Networks. Oxford, UK: Oxford University Press, 1979.

    MATH  Google Scholar 

  3. C. Chau, R. Gibbens, and T. G. Griffin, “Towards a unified theory of policy-based routing,” in Proc. IEEE INFOCOM, Barcelona, Spain, 2006, pp. 1–12.

  4. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd ed. Cambridge, USA: MIT Press. 2001.

    MATH  Google Scholar 

  5. L. Gao and J. Rexford, “Stable internet routing without global coordination,” IEEE/ACM Trans. Netw., vol. 9, no. 6, pp. 681–692, Dec. 2001.

    Article  Google Scholar 

  6. M. Gondran and M. Minoux, Graphs and Algorithms. Chichester, UK: Wiley, 1984.

    MATH  Google Scholar 

  7. M. Gondran and M. Minoux, Graphs, Dioids, and Semirings: New Models and Algorithms. New York, USA: Springer, 2008.

    MATH  Google Scholar 

  8. M. G. Gouda and M. Schneider, “Maximizable routing metrics,” IEEE/ACM Trans. Netw., vol. 11, no. 4, pp. 663–675, Aug. 2003.

    Article  Google Scholar 

  9. T. G. Griffin and A. J. T. Gurney, “Increasing bisemigroups and algebraic routing,” in 10th Int. Conf. Relational Methods in Computer Science (RelMiCS10), Frauenworth, Germany, 2008, pp. 123–137.

  10. L. Gao, T. G. Griffin, and J. Rexford, “Inherently safe backup routing with BGP,” in Proc. IEEE INFOCOM, Anchorage, USA, 2001, vol. 1, pp. 547–556.

    Google Scholar 

  11. T. G. Griffin and G. Huston, “RFC 4264: BGP Wedgies,” IETF, Nov. 2005.

  12. T. G. Griffin, A. D. Jaggard, and V. Ramachandran, “Design principles of policy languages for path vector protocols,” in Proc. ACM SIGCOMM, Karlsruhe, Germany, 2003, pp. 61–72.

  13. T. G. Griffin, F. B. Shepherd, and G. Wilfong, “The stable paths problem and interdomain routing,” IEEE/ACM Trans. Netw., vol. 10, no. 2, pp. 232–243, Apr. 2002.

    Article  Google Scholar 

  14. A. J. T. Gurney and T. G. Griffin, “Lexicographic products in metarouting,” in Proc. IEEE Int. Conf. Network Protocols (ICNP), Beijing, China, 2007, pp. 113–122.

  15. A. Gurney, “Construction and verification of routing algebras,” Ph.D. dissertation, Univ. Cambridge, 2009.

  16. S. Halabi and D. McPherson, Internet Routing Architectures, 2nd ed. Indianapolis, USA: Cisco Press, 2001.

    Google Scholar 

  17. G. Huston, “Interconnection, peering and settlements: Part I,” Internet Protocol J., vol. 2, no. 1, pp. 2–16, Mar. 1999.

    Google Scholar 

  18. G. Huston, “Interconnection, peering and settlements: Part II,” Internet Protocol J., vol. 2, no. 2, pp. 2–23, Jun. 1999.

    MathSciNet  Google Scholar 

  19. K. Varadhan, R. Govindan, and D. Estrin, “Persistent route oscillations in inter-domain routing,” Comput. Netw., vol. 32, no. 1, pp. 1–16, Jan. 2000.

    Article  Google Scholar 

  20. Z. M. Mao, L. Qiu, J. Wang, and Y. Zhang, “On as-level path inference,” in Proc. ACM SIGMETRICS, Banff, Canada, 2005, pp. 339–349.

  21. D. McPherson, V. Gill, D. Walton, and A. Retana. “RFC 3345: BGP Persistent Route Oscillation Condition”, IETF, Aug. 2002.

  22. Y. Rekhter, T. Li, and S. Hares, “RFC 4271: A Border Gateway Protocol 4 (BGP-4),” IETF, Jan. 2006.

  23. J. L. Sobrinho, “Algebra and algorithms for QoS path computation and hop-by-hop routing in the Internet,” IEEE/ACM Trans. Netw., vol. 10, no. 4, pp. 541–550, Aug. 2002.

    Article  Google Scholar 

  24. J. L. Sobrinho, “Network routing with path vector protocols: Theory and applications,” in Proc. ACM SIGCOMM, Karlsruhe, Germany, 2003, pp. 40–60.

  25. J. L. Sobrinho, “An algebraic theory of dynamic network routing,” IEEE/ACM Trans. Netw., vol. 13, no. 5, pp. 1160–1173, Oct. 2005.

    Article  Google Scholar 

  26. J. L. Sobrinho and T. G. Griffin, “Routing in equilibrium,” in 19th Int. Symp. Mathematical Theory of Networks and Systems (MTNS), Budapest, Hungary, 2010.

  27. I. van Beijnum, BGP: Building Reliable Networks with the Border Gateway Protocol. Sebastopol, USA: O’Reilly Media, 2002.

    Google Scholar 

  28. R. White, D. McPherson, and S. Sangli, Practical BGP. Boston, USA: Addison-Wesley, 2005.

    Google Scholar 

  29. R. Zhang and M. Bartell, BGP Design and Implementation. Indianapolis, USA: Cisco Press, 2003.007/s13119-011-0002-7

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, Cambridge, UK

    Timothy G. Griffin

Authors
  1. Timothy G. Griffin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Timothy G. Griffin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Griffin, T.G. Exploring the stratified shortest-paths problem. Netw.Sci. 1, 2–14 (2012). https://doi.org/10.1007/s13119-011-0003-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13119-011-0003-6

Keywords

Search

Navigation