Geometric Routing With Word-Metric Spaces

As a potential solution to the compact routing problem, geometric routing has been proven to be both simple and heuristically effective. These routing schemes assign some (virtual) coordinates in a metric space to each network vertex through the process called embedding. By forwarding packets to the closest neighbor to the destination, they ensure a completely local process with the routing table bounded in size by the maximum vertex degree. In this letter, we present an embedding of any finite connected graph into a metric space generated by algebraic groups, and we prove that it is greedy (guaranteed packet delivery). Then, we present a specialized compact routing scheme relying on this embedding for scale-free graphs. Evaluation through simulation on several Internet topologies shows that the resulting stretch remains below the theoretical upper bounds.