Uniform election in trees and polyominoids Original Research Article

Election is a classical paradigm in distributed algorithms. This paper aims to design and analyze a distributed algorithm choosing a node in a graph which models a network. In case the graph is a tree, a simple schema of algorithm acts as follows: it removes leaves until the graph is reduced to a single vertex; the elected one. In Métivier et al. (2003) , the authors studied a randomized variant of this schema which gives the same probability of being elected to each node of the tree. They conjectured that the expected election duration of this algorithm is image where image denotes the size of the tree, and asked whether it is possible to use the same algorithm to obtain a fair election in other classes of graphs.