Internet instability foiled by hyperbolic maths

Hidden Internet ‘black holes’ have been revealed as international scientists map the world’s data network onto hyperbolic space.

“They discovered a latent hyperbolic, or negatively curved, space hidden beneath the Internet’s topology, leading them to devise a method to create an Internet map using hyperbolic geometry,” said the San Diego Supercomputer Center. “The researchers say such a map would lead to a more robust Internet routing architecture because it simplifies path-finding throughout the network.”

Along with San Diego, researchers came from the University of California, San Diego, Universitat de Barcelona in Spain and the University of Cyprus.

“Internet routing today is based on a topographical map that does not take into account any geometric coordinates in any space,” said University of California researcher Dmitri Krioukov.

He believes purely topographic planning is not sustainable.

“It is very complicated, inefficient, and difficult to scale to the rapidly growing size of the Internet, which is now accessed by more than a billion people each day,” said Krioukov. “In fact, we are already seeing parts of the Internet become intermittently unreachable, sinking into so-called ‘black holes’, which is a clear sign of instability.”

By combining the hyperbolic theory with historic Internet data constantly gathered by the University of California, and statistical inference methods, the scientists built a geometric map of the Internet.

Results indicate that routing using such mapping would be superior purely topographic mapping.

Instead of perpetually accessing and rebuilding a reference list of all available network paths, each router in the Internet would know only its hyperbolic coordinates and the coordinates of its neighbours so it could route in the right direction, only relaying the information to its closest neighbour in that direction – known as ‘greedy routing’.

“We believe that using such a routing architecture based on hyperbolic geometry will create the best possible levels of efficiency in terms of speed, accuracy, and resistance to damage,” said Krioukov.

However the researchers caution that implementing and deploying such a routing structure in the Internet might be as challenging, if not more challenging, than discovering its hidden space.

“There are many technical and non-technical issues to be resolved before the Internet map that we found would be the map that the Internet uses,” said Krioukov.

The work is published this week in Nature Communications.

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