Distributed Voting in Beep Model

TL;DR

This paper introduces two algorithms for distributed multi-choice voting using beep signals in networks, providing theoretical guarantees and experimental validation of their effectiveness and robustness across various network conditions.

Contribution

The paper presents the first solutions for distributed majority voting in beep communication models, with proven convergence and high success probability.

Findings

Algorithms are invariant to network topology and size

High success probability as initial majority increases

Effective in practical applications like sensor networks

Abstract

We consider the problem of distributed multi-choice voting in a setting that each node can communicate with its neighbors merely by sending beep signals. Given its simplicity, the beep communication model is of practical importance in different applications such as system biology and wireless sensor networks. Yet, the distributed majority voting has not been resolved in this setting. In this paper, we propose two algorithms, named Distributed Voting with Beeps, to resolve this problem. In the first proposed algorithm, the adjacent nodes having the same value form a set called spot. Afterwards, the spots with majority value try to corrode the spots with non-majority values. The second proposed algorithm is based on pairwise interactions between nodes. The proposed algorithms have a termination detection procedure to check whether voting is achieved. We establish theoretical guarantees for the convergence of these algorithms. In particular, we show that the success probability of the first algorithm tends to one as the percentage of the initial votes in majority increases. For the second algorithm, we show that it returns the correct output with high probability. Our experiments show that the algorithms are fairly invariant to the network topology, initial distribution of values, and network size.