Symmetry Breaking in Anonymous Networks: Characterizations

We consider the problem of electing a leader in an an-onymous network of processors. More precisely our modelis that of a directed graph, with vertices corresponding toprocessors, and arcs to communication links (we freely in-terchange symmetric digraphs and undirected graphs). Wemake no assumption on the structure of the network: self-loopsand parallel arcs are allowed. In particular, processorsare anonymous: they do not have unique identifiers.We consider both synchronous and asynchronous pro-cessor activation models, and models with and without“port awareness” (local names for outgoing and/or for in-coming arcs). We consider both unidirectional and bidirec-tional links. Our models will be defined precisely in thesequel.It is well known that once a leader is found, many other