Lexicographic products in metarouting

Routing protocols often keep track of multiple route metrics, where some metrics are more important than others. Route selection is then based on lexicographic comparison: the most important attribute of each route is considered first, and if this does not give enough information to decide which route is better, the next attribute is considered; and so on. We investigate protocols that find globally optimal paths and protocols that find only locally optimal paths. In each case we characterize exactly when lexicographic products can be used to define well-behaved routing protocols. We apply our results to protocols that can partition a network into distinct administrative regions, such as OSPF areas and BGP autonomous systems. We show that in some cases this type of local autonomy is fully compatible with global optimality.