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In this paper, the authors consider the problem of monitoring detecting separation of agents from a base station in robotic and sensor networks. Such separation can be caused by mobility and/or failure of the agents. While separation/cut detection may be performed by passing messages between a node and the base in static networks, such a solution is impractical for networks with high mobility, since routes are constantly changing. They propose a distributed algorithm to detect separation from the base station. The algorithm consists of an averaging scheme in which every node updates a scalar state by communicating with its current neighbors. They prove that if a node is permanently disconnected from the base station, its state converges to 0.
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