How do I find my wife in a supermarket?
This is called rendezvous problem.

As the paper: Mobile Agent Rendezvous: A Survey mentioned, this problem is original proposed by Alpern: The Rendezvous Search Problem:


  Two astronauts land on a spherical body that is much larger than the
  detection radius (within which they can see each other). The body does
  not have fixed orientation in space, nor does it have an axis of rotation,
  so that no common notion of position or direction is available to
  the astronauts for coordination. Given unit walking speeds for both astronauts, how should they move about so as to minimize the expected
  meeting time T (before they come within the detection radius)?


In the survey paper above, 


  Abstract: Recent results on the problem of mobile agent rendezvous on distributed networks are surveyed with an emphasis on outlining the various approaches taken by researchers in the theoretical computer science community.


It covers both "Asymmetric Rendezvous" (in Section 4) and "Symmetric Rendezvous" (in Section 5).



For symmetric rendezvous, the paper by Alpern shows: 


  It is shown how symmetries in the search region may hinder the process by preventing coordination based on concepts such as north or clockwise.