As the Internet continues to grow, it may be in everyone's best interest to organize how its various parts connect to each other, according to a paper published in Nature Communications. A group of researchers have developed a system that structures the Internet's nodes by coordinates, and allows each node to send information through a short hyperbolic path by knowing only which of its neighboring nodes will get the information closer to its destination. While the theoretical implementation works almost perfectly, the geographical realities of the Internet's arrangement suggest that efficient, scalable arrangements like this one may never come to pass.

The Internet, such as it is, is a series of autonomous systems (AS, not tubes). An individual AS can be viewed as any part of the Internet owned and maintained by a single entity, and can range in size from a single person to AT&T. Connections between autonomous systems are what allow information on the Internet to get around, and a few groups of researchers are beginning to see the disjointed business arrangements between autonomous systems as a potential problem.

So far, there are no rules about how autonomous systems connect to one another, and each AS makes business partnerships with others as a matter of convenience. Still, each AS needs to be able to reach every other AS out there, and has to maintain connections that will allow this to happen. Since the AS population is growing at a rate of 2,400 nodes every year, this could create a pretty tangled web of routing information.

Since there are no signs of slackening growth, the Internet might benefit from some organization. A group of researchers set out to map the various autonomous systems, giving each a set of static coordinates and allowing them to relate to each other in a way that doesn't change based on new or souring business relationships.

The disc-shaped map is organized not unlike a top-down view of a tree, with AS connections branching out from the center. To get information from one AS to another, the information travels in the smallest possible hyperbola, or arc, using a system called "greedy forwarding."

Greedy forwarding is based on the desire to get information around in as short a distance as possible, while forcing each node to maintain very little information—nothing beyond the coordinates of its neighbors. If a node holds information, it checks the destination coordinate against those of its neighbors, and then sends the info on to the neighbor that is nearest to the destination. After a series of similar transitions, the information arrives without anyone having to chart the whole route.

To get information from one AS in the hinterlands of the Internet (the Hinternet, if you will) to another similarly peripheral one, the information would travel up the branches to the nearest common node, and then back down. Many of the paths on the map form hyperbolas like this, giving the hyperbolic map its name.

The researchers found that the hyperbolic paths were sufficiently short to compete with the current Internet topology. They also wouldn't overload any particular AS with traffic, provided the map is set up so that appropriately large autonomous systems occupy the most central spots. Using simple greedy forwarding, the authors found they had a success rate of 97 percent, and even higher rates with more complicated greedy forwarding processes.

But the design was not without problems. Failures of central autonomous systems in this arrangement could be catastrophic. However, the authors noted that larger autonomous systems tend to have thousands of routers, so it would be unlikely for them all to be brought down simultaneously. Still, if an interested party wanted to bring a large AS to its knees, strategically downing the right number of routers might overload the others and take them down as well.

The more significant problem for the hyperbolic map is that it does not agree well with physical reality. Applying the hyperbolic map to a non-hyperbolic space—i.e. the world—was much less successful. Information sent through the geographically structured map had a success rate of only 30 percent. This may be a result of the autonomous systems' routers being much more scattered geographically than their single assigned coordinate would suggest.

While the hyperbolic map system is robust as long as certain ideal conditions are fulfilled, and is much more scalable than the Internet's current arrangement, it appears to not be meant for this world. An implementation that would actually work would involve serious rearrangements of autonomous systems' resources, and would need to compel certain business relations between them.

The authors acknowledge that the aspect of their system that needs the most work is the method for mapping, and they are currently working on another type of layout that fits more closely with the physical realities of AS positioning.

Nature Communications, 2010. DOI: 10.1038/ncomms1063 (About DOIs).