PrimeTime: A Finite-Time Consensus Protocol for Open Networks

In distributed problems where consensus between agents is required but average consensus is not desired, it can be necessary for each agent to know not only the data of each other agent in the network, but also the origin of each piece of data before consensus can be reached. However, transmitting large tables of data with IDs can cause the size of an agent's message to increase dramatically, while truncating down to fewer pieces of data to keep the message size small can lead to problems with the speed of achieving consensus. Also, many existing consensus protocols are not robust against agents leaving and entering the network. We introduce PrimeTime, a novel communication protocol that exploits the properties of prime numbers to quickly and efficiently share small integer data across an open network. For sufficiently small networks or small integer data, we show that messages formed by PrimeTime require fewer bits than messages formed by simply tabularizing the data and IDs to be transmitted.