| Summary: | Introducing leadership and mobility is known to benefit wireless sensor networks in terms of consensus-building and collective decision-making. However, these benefits are neither analytically proven nor quantified in the literature. This paper fills this gap by investigating the mobility dynamics in wireless sensor networks analytically. The results of the analytical investigation are presented as a set of theorems and their proofs. This paper also establishes a natural synergy between the leader-follower model and its bipartite graph representation. It demonstrates the advantages of the leader-follower model for consensus-building over others in terms of improved convergence rate. It presents a strategy for choosing leaders from among the agents participating in the consensus-building process using the well-known graph-coloring solution. Then, it shows how the leader-follower model helps improve the convergence rate of consensus-building. Finally, it shows that the convergence rate of the consensus-building process can be further improved by making the leaders mobile.
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