In many respects pathfinding algorythms like A star for finding the shortest route though graphs are similar to the pathfinding on the internet when routing trafic.

However the pathfinding routers perform seem to have remarkable properties. As I understand it:

It's very perfromant.

New nodes can be added at any time that use a free address from a finite (not tree like) address space.

It's real routing, like A*, theres never any doubling back for example.

IP addresses don't have to be geographicly nearby.

The network reacts quickly to changes to the networks shape, for example if a line is down.

Routers share information and it takes time for new IP's to be registered everywhere, but presumably every router dosn't have to store a list of all the addresses each of it's directions leads most directly to.

I can't find this information elsewhere however I don't know where to look or what search tearms to use. I'm looking for a basic, general, high level description to the algorithms workings, from the point of view of an individual router.