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Article Dans Une Revue Discrete Applied Mathematics Année : 2010

Uniform Election in Trees and Polyominoids

Résumé

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 till the graph is reduced to a single vertex: the elected one. In \cite{MSZ03}, 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 expected election duration of this algorithm is $O(\ln(n))$ where $n$ 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. In this paper, we prove their conjecture. We then introduce a new structure called polyominoid graphs. We show how a spanning tree for these graphs can be computed locally so that our algorithm, applied to this spanning tree, gives a uniform election algorithm on polyominoids.

Domaines

Autre [cs.OH]

Dates et versions

hal-00451114 , version 1 (28-01-2010)

Identifiants

Citer

Abdelaaziz El Hibaoui, John Michael Robson, Nasser Saheb-Djahromi, Akka Zemmari. Uniform Election in Trees and Polyominoids. Discrete Applied Mathematics, 2010, 158, pp.981-987. ⟨10.1016/j.dam.2010.01.008⟩. ⟨hal-00451114⟩

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