Subjective-Cost Policy Routing

We study a model of interdomain routing in which autonomous systems’ (ASes’) routing policies are based on subjective cost assessments of alternative routes. The routes are constrained by the requirement that all routes to a given destination must be confluent. We show that it is NP-hard to determine whether there is a set of stable routes. We also show that it is NP-hard to find a set of confluent routes that minimizes the total subjective cost; it is hard even to approximate minimum cost closely. These hardness results hold even for very restricted classes of subjective costs. We then consider a model in which the subjective costs are based on the relative importance ASes place on a small number of objective cost measures. We show that a small number of confluent routing trees is sufficient for each AS to have a route that nearly minimizes its subjective cost. We show that this scheme is trivially strategyproof and that it can be computed easily with a distributed algorithm that does not require major changes to the Border Gateway Protocol. Furthermore, we prove a lower bound on the number of trees required to contain a (1 + )-approximately optimal route for each node and show that our scheme is nearly optimal in this respect.