Last week I heard some informatic students talking about car-to-car communication via wifi-hotspots in cars and the following problem occured to me:
Suppose you are making a road trip with many friends and multiple cars and for some reason, all cars in the world are equipped with their own local wifi-hotspot. Obviously you don't want to call your friends in the other cars using cellphones (too expensive). Being a group of nerdy computer scientists, you wrote a chat application that uses the wifi-hotspots from cars in your neighbourhood to communicate for free!
All is well untill the dumb friend decides to pick up a shady looking hitchhiker armed with several blood-spattered axes. Anyway, as the distance between your cars grows larger, you lose a direct communication path. How do you establish and maintain communication with your friends' car using only the local wifi-hotspots of all cars?
Let's state this problem in a more mathematical language: Suppose you are given a time dependent (directed) graph and every vertex only has local information on this graph (it only sees close neighbours). Suppose you are riding on some vertex $A$ and you want to send a message to vertex $B$ but you don't know where vertex $B$ is.
Can you, under reasonable assumptions, find vertex $B$ and communicate with it? Preferably you try to keep said communication channel alive as long as possible. If so, what is a reasonable algorithm or idea to do this?
Also, is there any reasonable variant of this problem that can be "solved" using some interesting tools from linear algebra (such as eigenvectors)?
Perhaps I should point out that the following paper seems related but is not really what I hoped for. I'm more interested in basic linear algebra or elementary ideas that can help to tackle such problems. I'm not very interested in the technical implementation of such algorithms and their complexity.