Locally guided randomized elections in trees: The totally fair case

We design and analyze a randomized one-passage election algorithm in trees based on a result of Angluin in [Proceedings of the 12th Symposium on Theory of Computing, 1980, p. 82]. The election process is a distributed elimination scheme which removes leaves one-by-one reducing the tree to a single vertex, called the leader (or elected vertex). We define a locally computable parameter guiding randomly the elimination process. As a particular instance, we provide a parameter assignment in a Markovian type random process in which all vertices have the same chance of being elected.