On Distributed Cardinality Estimation: Random Arcs Recycled

Abstract

We introduce and analyze a distributed cardinality estimation algorithm for a network consisted of not synchronized nodes. Our solution can be regarded as a generalization of the classic approximate counting algorithm based on the balls and bins model and is connected to the well studied process of covering the circle with random arcs. Although the algorithm is presented in the context of a radio network, the basic idea is applicable to any system in which many uncoordinated nodes communicate over a shared medium. In the paper we prove the correctness of the algorithm and by the methods of complex analysis we carefully examine the accuracy and precision of the estimator we have proposed. We also show that the construction of the proposed algorithm is a backbone for simple distributed summation.

Distributed Voting in Beep Model

“…Although beep model is almost a newly developed communication protocol, it has been received much attention in recent years and various algorithms have been proposed for different distributed problems in this model. As examples of these problems, we can mention interval coloring and graph coloring [5], [14], [15], [16], leader election [17], [18], [19], [20], [21], [22], [23], maximal independent set [24], [25], [26], [27], [28], [29], minimum connected dominating set [30], network size approximation and counting [31], [32], [33], [34], deterministic rendezvous problem [35], naming problem [36], membership problem [37], [38], broadcasting [39], [40], [41], and consensus [42].…”