  Two anonymous mobile agents navigate synchronously in an anonymous graph and
have to meet at a node, using a deterministic algorithm. This is a symmetry
breaking task called rendezvous, equivalent to the fundamental task of leader
election between the agents. When is this feasible in a completely anonymous
environment? It is known that agents can always meet if their initial positions
are nonsymmetric, and that if they are symmetric and agents start
simultaneously then rendezvous is impossible. What happens for symmetric
initial positions with non-simultaneous start? Can symmetry between the agents
be broken by the delay between their starting times?
  In order to answer these questions, we consider {\em space-time initial
configurations} (abbreviated by STIC). A STIC is formalized as
$[(u,v),\delta]$, where $u$ and $v$ are initial nodes of the agents in some
graph and $\delta$ is a non-negative integer that represents the difference
between their starting times. A STIC is {\em feasible} if there exists a
deterministic algorithm, even dedicated to this particular STIC, which
accomplishes rendezvous for it. Our main result is a characterization of all
feasible STICs and the design of a universal deterministic algorithm that
accomplishes rendezvous for all of them without {\em any } a priori knowledge
of the agents. Thus, as far as feasibility is concerned, we completely solve
the problem of symmetry breaking between two anonymous agents in anonymous
graphs. Moreover, we show that such a universal algorithm cannot work for all
feasible STICs in time polynomial in the initial distance between the agents.
