Distributed Voting in Beep Model

Abstract

In this paper, we propose two distributed algorithms, named Distributed Voting with Beeps (DVB), for multi-choice voting in beep model where each node can communicate with its neighbors merely by sending beep signals. The two proposed algorithms have simple structures and can be employed in networks having severe constraints on the size of messages. 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 show that the probability of success of the first algorithm goes to one as the percentage of nodes choosing the majority vote as their initial values gets close to one. The second algorithm returns the correct vote with high probability. Our experiments show that the algorithms are fairly invariant to the network topology, initial distribution of values, and network size.