Absorbing lexicographic products in metarouting

Abstract

Modern treatments of routing protocols use algebraic techniques to derive the protocol’s properties, permitting a semantic richness more flexible than simple numerical “shortest paths”. Many such routing protocols make preference decisions based on multiple criteria. This fits well with an algebraic formulation with each strata in the decision process modeled as an algebraic structure, that are combined to create the full routing protocol. Routing protocols constructed in this manner are the focus of this paper. To implement such a routing protocol we must understand the properties needed on each of the algebraic formulations representing a strata. In this paper we examine a stratified routing algebra based on a recently suggested absorbing product and provide the necessary and sufficient conditions required by each of the operands to guarantee that such a routing language ensures globally optimal paths will be found.