With an aim to stress the need for a rigorous formalization of routing schemes for structured peer-to-peer overlay networks, in this work, we demonstrate the usefulness of a formal definition that we have come up with, by elaborating on one of the several network properties that are either determined or limited by the routing scheme that builds the network. After briefly presenting the intuition behind the necessity and sufficiency of our formal definition of a routing scheme for structured overlay networks, we elaborate on the notion of average path length for structured overlays and derive its expression in terms of the routing scheme parameters to show how the overlay network's average path length is determined by its routing scheme.
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