Efficient data aggregation is crucial for mobile wireless sensor networks, as their resources are significantly constrained. Over recent years, the average consensus algorithm has found a wide application in this technology. In this paper, we present a weight matrix simplifying the average consensus algorithm over mobile wireless sensor networks, thereby prolonging the network lifetime as well as ensuring the proper operation of the algorithm. Our contribution results from the theorem stating how the Laplacian spectrum of an undirected simple finite graph changes in the case of adding an arbitrary edge into this graph. We identify that the mixing parameter of Best Constant weights of a complete finite graph with an arbitrary order ensures the convergence in time-varying topologies without any reconfiguration of the edge weights. The presented theorems and lemmas are verified over evolving graphs with various parameters, whereby it is demonstrated that our approach ensures the convergence of the average consensus algorithm over mobile wireless sensor networks in spite of no edge reconfiguration.

No abstract

No abstract

No abstract

Abstract.

The exact information about the network size is crucial for the proper functioning of many distributed algorithms. In this paper, we analyze the average consensus algorithm for a distributed network size estimation bounded by the stopping criterion proposed for the wireless sensor networks. We analyze its four initial configurations over random geometric graphs of different connectivity under various parameters of the implemented stopping criterion. The performance is evaluated by the mean square error and the convergence rate expressed as the iteration number for the consensus. Finally, the results obtained under various conditions are compared to find the best performing configuration of both the average consensus algorithm and the implemented stopping criterion. Also, the results are compared to the distributed summing functionality.

Determining the network size is a critical process in numerous areas (e.g., computer science, logistic, epidemiology, social networking services, mathematical modeling, demography, etc.). However, many modern real-world systems are so extensive that measuring their size poses a serious challenge. Therefore, the algorithms for determining/estimating this parameter in an effective manner have been gaining popularity over the past decades. In the paper, we analyze five frequently applied distributed consensus gossip-based algorithms for network size estimation in multi-agent systems (namely, the Randomized gossip algorithm, the Geographic gossip algorithm, the Broadcast gossip algorithm, the Push-Sum protocol, and the Push-Pull protocol). We examine the performance of the mentioned algorithms with bounded execution over random geometric graphs by applying two metrics: the number of sent messages required for consensus achievement and the estimation precision quantified as the median deviation from the real value of the network size. The experimental part consists of two scenarios—the consensus achievement is conditioned by either the values of the inner states or the network size estimates—and, in both scenarios, either the best-connected or the worst-connected agent is chosen as the leader. The goal of this paper is to identify whether all the examined algorithms are applicable to estimating the network size, which algorithm provides the best performance, how the leader selection can affect the performance of the algorithms, and how to most effectively configure the applied stopping criterion.

No abstract