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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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
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