A Simple and Scalable Algorithm for Alignment in Broadcast Networks

We consider the problem of coordinating a group of mobile nodes communicating through a wireless medium. The objective of the network is the alignment of all the nodes towards a common direction through local interactions, without the need for global knowledge such as the network topology or the maximum degree of the network, or even local parameters, such as the number of neighbors. The key feature of our algorithm is that each node state update is done through voting, where the probability of each vote is biased by the state of the node neighbors. We propose two possible physical implementations for our algorithm. The first is based on the explicit exchange of packetized messages, while the second is a cross-layer approach. Our analysis unveils key convergence properties of this simple class of alignment algorithms, via analytical and simulated results.