Hop-by-hop Routing Convergence Analysis Based on Paths Algebra

This article reviews the paths algebra and analyses the hop-by-hop routing convergence either for a monoconstraint or multiconstraint case, verifying that, unlike what is indicated in the literature, even though isotonicity and monotonicity properties are important for building the routing trees, they are not sufficient to ensure the hop-by-hop routing convergence. In this investigation, we propose a new property, here named stability, as necessary and sufficient to ensure this convergence.