Accurate and Efficient Counting in Dynamic Networks

Dynamic network is the abstraction of networks with frequent topology changes arising from node mobility or other reasons. With the model of dynamic network, fundamental distributed computing problems can be formally studied with rigorous correctness. In this work, we study the counting problem, which plays a significant role in many applications, such as all-to-all information dissemination. Existing counting algorithms for dynamic networks are mostly estimation based and randomized, and cannot achieve accurate results deterministically. To address this problem, we adopt the diffusing computation approach in this paper. Although this approach has been widely used to solve different distributed computing problems, due to dynamic topology changes, existing diffusing computation algorithms cannot work under dynamic network models. To address such challenge, we firstly define a new dynamicity model, named (Q, S)-distance, which is used to describe dynamic changes of information propagation time. Based on (Q, S)-distance, we design two different counting algorithms. The first algorithm focuses on extending typical diffusing computation approach by handling topology changes. Different from existing algorithms, which have two phases, our algorithms contain three phases and the new phase is used to determine and notify the termination of tree growing, which the major challenge is caused by topology dynamicity. The second algorithm further extends the first one by incorporating a cluster-based hierarchy to reduce communication cost. The correctness of both the algorithms is formally proved and their performances in time cost and communication cost are analyzed.