Metarouting allows for the modeling of routing protocols using an algebraic structure called routing algebra. Routing protocols requiring design or validation can easily be modeled using this approach. To date, however, existing research on routing algebras has mainly focused on applying this approach to routing protocols that are generally used in networks which have a single addressing and forwarding protocol. The basic algebraic structures used in such contexts are semirings, Sobrinho’s algebras and algebras of endomorphisms. In this paper, we propose the modification of these existing routing algebras to deal with networks that contain multiple forwarding protocols where tunnels are omnipresent. To achieve this, we define new algebraic structures derived from the three aforementioned ones, in order to model the generalized routing problem with automatic tunneling entitled valid paths algebra. All of our routing algebras are defined as semi-direct products of two structures, the well-known shortest paths algebra and the proposed valid paths algebra. These new algebras are isotonic and non-monotonic with a partial order. We propose a fixed point for those new algebras and we prove the iterative convergence to the optimal solution of the valid shortest paths problem.

中文翻译：

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多层网络中具有自动隧道的元路由


元路由允许使用称为路由代数的代数结构对路由协议进行建模。使用这种方法可以轻松地对需要设计或验证的路由协议进行建模。然而，迄今为止，现有的路由代数研究主要集中于将这种方法应用于通常在具有单一寻址和转发协议的网络中使用的路由协议。在这种情况下使用的基本代数结构是半环、索布里尼奥代数和自同态代数。在本文中，我们建议修改这些现有的路由代数，以处理包含多种转发协议且隧道无处不在的网络。为了实现这一目标，我们定义了从上述三个代数结构派生的新代数结构，以便使用名为有效路径代数的自动隧道对广义路由问题进行建模。我们所有的路由代数都被定义为两种结构的半直积，即众所周知的最短路径代数和提出的有效路径代数。这些新代数是等调的且具有偏序的非单调性。我们为这些新代数提出了一个不动点，并证明了有效最短路径问题最优解的迭代收敛性。