Election and rendezvous with incomparable labels

In “Can we elect if we cannot compare” (SPAA’03), Barrière, Flocchini, Fraigniaud and Santoro consider a qualitative model of distributed computing, where the labels of the entities are distinct but mutually incomparable. They study the leader election problem in a distributed mobile environment and they wonder whether there exists an algorithm such that for each distributed mobile environment, it either states that the problem cannot be solved in this environment, or it successfully elects a leader. In this paper, we give a positive answer to this question. We also give a characterization of the distributed mobile environments where election and rendezvous can be solved.