The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing
scheme delivering a nearly optimal local memory upper bound. Using both direct
analysis and simulation, we calculate the stretch distribution of this routing
scheme on random graphs with power-law node degree distributions, Pk​∼k−γ. We find that the average stretch is very low and virtually
independent of γ. In particular, for the Internet interdomain graph,
γ∼2.1, the average stretch is around 1.1, with up to 70% of paths
being shortest. As the network grows, the average stretch slowly decreases. The
routing table is very small, too. It is well below its upper bounds, and its
size is around 50 records for 104-node networks. Furthermore, we find that
both the average shortest path length (i.e. distance) dˉ and width of
the distance distribution σ observed in the real Internet inter-AS graph
have values that are very close to the minimums of the average stretch in the
dˉ- and σ-directions. This leads us to the discovery of a unique
critical quasi-stationary point of the average TZ stretch as a function of
dˉ and σ. The Internet distance distribution is located in a
close neighborhood of this point. This observation suggests the analytical
structure of the average stretch function may be an indirect indicator of some
hidden optimization criteria influencing the Internet's interdomain topology
evolution.Comment: 29 pages, 16 figure