>If I live in London and the distance from me to Paris is 50.000 km, and you live in Rome, 70.000 km from Paris, that does not give me enough to calculate the distance between Rome and London.

Yes, but you do know that the distance from London to Rome is less than 12,000 km, because of the triangle inequality axiom. So if that's too far, that search path is discarded.

Then we just start the process over again, by comparing each subtree back to the original location.