COMPLEXNETROUTING · Efficient Routing in the Internet and other Complex Networks using Hyperbolic Metric Spaces

The lack of predictive power over complex systems,either designed by humans or evolved by nature, is afoundational problem in contemporary science. The Internetoffers a paradigmatic example: nothing in its architecture anddesign explains its complex large-scale structure, unexpectedlydiscovered decades after its inception. We face an unsettlingtruth: the Internet has acquired emergent properties that arebeyond our full understanding, much less control.As scientists, we are compelled to explore how the peculiarstructure relates to the function(s) of complex networks.Many complex networks in nature share the peculiar structuralcharacter of the Internet, but they also manifest phenomenalbehavior: they efficiently route information without any routingcommunication protocol, i.e., without any knowledge of the globalnetwork topology. This achievement is currently beyond the reachof man-made networks; the Internet still uses a 30-year old routingarchitecture with fundamentally unscalable overhead requirements.The only known mechanism for efficient routing without globaltopology knowledge is greedy routing in a network embeddedin a metric space. We propose to explore the hypothesis that beneath theobservable topologies of complex networks reside hidden hyperbolic metric spaces,which could be used to facilitate maximally efficient routing withscalability characteristics either equal, or close to, theoretically best possible.