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Increasing Bisemigroups and Algebraic Routing

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Book cover Relations and Kleene Algebra in Computer Science (RelMiCS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4988))

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Abstract

The Internet protocol used today for global routing — the Border Gateway Protocol (BGP) — evolved in a rather organic manner without a clear theoretical foundation. This has stimulated a great deal of recent theoretical work in the networking community aimed at modeling BGP-like routing protocols. This paper attempts to make this work more accessible to a wider community by reformulating it in a purely algebraic setting. This leads to structures we call increasing bisemigroups, which are essentially non-distributive semirings with an additional order constraint. Solutions to path problems in graphs annotated over increasing bisemigroups represent locally optimal Nash-like equilibrium points rather than globally optimal paths as is the case with semiring routing.

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Authors and Affiliations

  1. Computer Laboratory, University of Cambridge,  

    Timothy G. Griffin & Alexander J. T. Gurney

Authors
  1. Timothy G. Griffin
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  2. Alexander J. T. Gurney
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Editor information

Rudolf Berghammer Bernhard Möller Georg Struth

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© 2008 Springer-Verlag Berlin Heidelberg

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Griffin, T.G., Gurney, A.J.T. (2008). Increasing Bisemigroups and Algebraic Routing. In: Berghammer, R., Möller, B., Struth, G. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2008. Lecture Notes in Computer Science, vol 4988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78913-0_11

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  • DOI: https://doi.org/10.1007/978-3-540-78913-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78912-3

  • Online ISBN: 978-3-540-78913-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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