On the Dynamics of Branching Random Walk on Random Regular Graph

Several popular problems in information networking and social networking such as search, distribution, and dissemination can be modeled by random walk of single or multiple agents on a graph. As an approach to remedy the redundancy in multiple random walks, Branching Random Walk (BRW) has been proposed, in which the number of agents of random walks is dynamically changed by the branching-and-aggregation mechanism. An agent starting its walk from an originating node randomly selects b nodes among its neighbor nodes, and it activates those neighbor nodes (branching). If multiple agents simultaneously visit the same node, those agents are unified into a single agent (aggregation). BRW is a relatively new mobility model on a graph. Hence, to the best of our knowledge, understanding of its dynamical properties is quite limited. In this paper, we describe the dynamics of BRW on a random regular graph, and clarify the relation between the branching parameter b and the mean and the distribution of hitting times and the mean cover time.