Compact routing on internet-like graphs

Abstract

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, P k ∼ 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 10 4 -node networks. Furthermore, we find that both the average shortest path length (i.e. distance) d 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 d-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 d 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. * dima@krioukov.net † kfall@intel-research.net ‡ yxw@mit.edu RoutingSince the pioneering work by Kleinrock and Kamoun,[55], the trade-off between stretch 1 and the amount of routing information (i.e. memory space) required by a routing scheme has been understood, analyzed, and improved. Many relatively recent "Internet routing architecture" proposals, [16,54], are based on the ideas of [55]. Since [55] was the first work of its type, it is not surprising that naïve routing based on it would generate stretch that is far from optimal. Indeed, the simple calculations presented in Appendix A show that the stretch produced by [55] on the present Internet interdomain graph would be of the order of 10.However, the high value of stretch was not the central problem with [55]. This work along with the works that closely followed it, [56,77], concentrated on optimal hierarchical network clustering (splitting into areas) satisfying a set of assumptions, but no proof of existence of such clustering for generic graphs and no algorithm to find it when it exists were obtained. While several subsequent works tried to overcome these problems, all known hierarchical routing schemes eventually turned out to be inferior with respect to more recent direct routing schemes. 2 In the work by Peleg and Upfal, [76], the trade-off between memory space and stretch for generic 3 networks was rigourously analyzed for the first time. The work contained several issues that were addressed in many publications that followed [76]. One of the issues was that only the total (per network) space was bounded, the local (per node) space was unbounded. Another issue was that the ...

On the Scalability of Path Exploration Using Opportunistic Path-Vector Routing

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Harnessing Internet topological stability in Thorup-Zwick compact routing

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