An efficient message passing election algorithm based on Mazurkiewicz's algorithm

We study the election and the naming problems in the asynchronous message passing model. We present a necessary condition based on Angluin's lifting lemma [1] that must be satisfied by any network that admits a naming (or an election) algorithm. We then show that this necessary condition is also sufficient: we present an election and naming algorithm based on Mazurkiewicz's algorithm [17]. The algorithm we obtained is totally asynchronous and it needs a polynomial number of messages of polynomial size, whereas previous election algorithms in this model are pseudo-synchronous and use messages of exponential size.