Faster Supervised Average Consensus in Adversarial and Stochastic Anonymous Dynamic Networks

Abstract

How do we reach consensus on an average value in a dynamic crowd without revealing identity? In this work, we study the problem of average network consensus in Anonymous Dynamic Networks (ADN). Network dynamicity is specified by the sequence of topology-graph isoperimetric numbers occurring over time, which we call the isoperimetric dynamicity of the network. The consensus variable is the average of values initially held by nodes, which is customary in the network-consensus literature. Given that having an algorithm to compute the average one can compute the network size (i.e., the counting problem) and vice versa, we focus on the latter. We present a deterministic distributed average network consensus algorithm for ADNs that we call isoperimetric Scalable Coordinated Anonymous Local Aggregation, and we analyze its performance for different scenarios, including worst-case (adversarial) and stochastic dynamic topologies. Our solution utilizes supervisor nodes, which have been shown to be necessary for computations in ADNs. The algorithm uses the isoperimetric dynamicity of the network as an input, meaning that only the isoperimetric number parameters (or their lower bound) must be given, but topologies may occur arbitrarily or stochastically as long as they comply with those parameters. Previous work for adversarial ADNs overestimates the running time to deal with worst-case scenarios. For ADNs with given isoperimetric dynamicity, our analysis shows improved performance for some practical dynamic topologies, with cubic time or better for stochastic ADNs, and our experimental evaluation indicates that our theoretical bounds could not be substantially improved for some models of dynamic networks.