Subjective-cost policy routing

  • Authors:
  • Joan Feigenbaum;David R. Karger;Vahab S. Mirrokni;Rahul Sami

  • Affiliations:
  • Yale University Computer Science Department, 51 Prospect St., New Haven, CT 06511, USA;MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St, Cambridge, MA 02139, USA;MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St, Cambridge, MA 02139, USA;University of Michigan School of Information, 1075 Beal Ave., Ann Arbor, MI 48109, USA

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

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Abstract

We study a model of path-vector routing in which nodes' 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 the 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 nodes place on a small number of objective cost measures. We show that a small number of confluent routing trees is sufficient for each node to have a route that nearly minimizes its subjective cost. We show that this scheme is trivially strategy proof and that it can be computed easily with a distributed algorithm. Furthermore, we prove a lower bound on the number of trees required to contain a (1+@e)-approximately optimal route for each node and show that our scheme is nearly optimal in this respect.