The Internet's routing system is facing stresses due to its poor fundamental scaling properties. Compact routing is a research field that studies fundamental limits of routing scalability and designs algorithms that try to meet these limits. In particular, compact routing research shows that shortest-path routing, forming a core of traditional routing algorithms, cannot guarantee routing table (RT) sizes that on all network topologies grow slower than linearly as functions of the network size. However, there are plenty of compact routing schemes that relax the shortest-path requirement and allow for improved, sublinear RT size scaling that is mathematically provable for all static network topologies. In particular, there exist compact routing schemes designed for grids, trees, and Internet-like topologies that offer RT sizes that scale logarithmically with the network size.

In this paper, we demonstrate that in view of recent results in compact routing research, such logarithmic scaling on Internet-like topologies is fundamentally impossible in the presence of topology dynamics or topology-independent (flat) addressing. We use analytic arguments to show that the number of routing control messages per topology change cannot scale better than linearly on Internet-like topologies. We also employ simulations to confirm that logarithmic RT size scaling gets broken by topology-independent addressing, a cornerstone of popular locator-identifier split proposals aiming at improving routing scaling in the presence of network topology dynamics or host mobility. These pessimistic findings lead us to the conclusion that a fundamental re-examination of assumptions behind routing models and abstractions is needed in order to find a routing architecture that would be able to scale "indefinitely."