Election algorithms with random delays in trees

TL;DR

This paper studies randomized election algorithms in trees where nodes are eliminated probabilistically until one remains, providing formulas for election probabilities in specific cases.

Contribution

It introduces a class of randomized algorithms for tree election and derives explicit formulas for election probabilities in certain algorithm categories.

Findings

Formulas for election probabilities in specific algorithm classes

Analysis of leaf elimination process in randomized election algorithms

Insights into probability distributions used by leaves

Abstract

The election is a classical problem in distributed algorithmic. It aims to design and to analyze a distributed algorithm choosing a node in a graph, here, in a tree. In this paper, a class of randomized algorithms for the election is studied. The election amounts to removing leaves one by one until the tree is reduced to a unique node which is then elected. The algorithm assigns to each leaf a probability distribution (that may depends on the information transmitted by the eliminated nodes) used by the leaf to generate its remaining random lifetime. In the general case, the probability of each node to be elected is given. For two categories of algorithms, close formulas are provided.