Error bounds for hierarchical routing

Abstract

We present a general model of hierarchical routing, with multiple levels of hierarchy, which introduces the concept of a cluster estimator to approximate the distance from a border node of a cluster to any node in the cluster. We characterize the hierarchical path length cHE and prove that the average error is minimized using the overall best routing cluster estimator. We present the first worst case upper bound on the error cHE - c* in hierarchical routing that is valid for any cluster estimator, and show the bound is sharp for two-level networks.