Inference on random graph, with an application to mobile sensors

Question

I've attended a course on Machine Learning and another one in Network Analysis, and I wonder if this two topics already intersect, in particular I'm interested in the following model:

• we have a mobile network (that is, the nodes perform a random walk in some area, then sending a message within some assigned range, let's say with radius r, communicating with every other node that in that moment is in that range).
• we take the point of view of a node and would like to infer as much as we can about the whole network (under suitable assumption, for example knowing or not knowing the total number of nodes, etc.), possibly in order to perform some achieved probabilistic version of well known distributed algorithm.

Are there results with respect to this scenario?

Answer 1

Interesting problem.

If we assume that each message exchanged between pairs of nodes contain summary information about every other exchange that has happened, for example, ID and status or ID and last known location.

In that case, any single node will have access to information about other nodes, and the number of nodes that any node has information on will increase as a function of time.

The closest analogy to this is from statistical mechanics, where over time, the number of collisions between distinct particles increases, to the point where with probability 1, every node has some (perhaps out of date) information about every other node.