Probabilistic analysis of an election algorithm in a tree
In this paper we consider the well-known case of election in a tree, and we study the probability for any vertex of a given tree to be elected. In particular, we show that if we consider the probability distribution based on the comparison of the election probabilities of neighbour vertices, there is one or two vertices having the highest probability of being elected. We give a very simple algorithm to compute these vertices, and we prove that in fact they are the medians.
Exact computations are done for special families of trees as filiform trees, wheels and crystals.
KeywordsElection Labelled Graphs Median Probabilistic analysis Tree
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