From Non-Optimal Routing Protocols to Routing on Multiple Optimality Criteria

At a suitable level of abstraction, all that standard routing protocols do is iterate extension and election operations on path attributes. An extension operation composes the attribute of a path from those of a link and another path, while an election operation produces the most preferred attribute of a set of candidate attributes, given a total order on them. These protocols are guaranteed to compute optimal paths only if the extension operation and the total order are entwined by the algebraic property of isotonicity, which states that the relative preference between two attributes is not inverted when both are extended by a third attribute. We solve the problem of computing and routing on optimal paths with generality by recognizing that every total order contains a partial order for which isotonicity holds. Then, we design a partial-order vectoring protocol where every election operation produces a subset of attributes from a set of candidate attributes, rather than a single attribute as is the case with a standard vectoring protocol; the election operation is derived from the partial order, ensuring that no attribute of the set of candidate attributes is preferred to an attribute of the elected subset. Moreover, we show how partial-order vectoring protocols can be designed to allow routing on optimal paths concurrently for diverse optimality criteria. Our evaluation over publicly available network topologies and attributes, covering both intra- and inter-AS routing, evince that the sizes of elected subsets of attributes are surprisingly small and that the partial-order vectoring protocol converges fast, sometimes faster than a standard vectoring protocol operating in the absence of isotonicity.