  In this paper we 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. We 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. We prove that if a node is permanently disconnected
from the base station, its state converges to $0$. If a node is connected to
the base station in an average sense, even if not connected in any instant,
then we show that the expected value of its state converges to a positive
number. Therefore, a node can detect if it has been separated from the base
station by monitoring its state. The effectiveness of the proposed algorithm is
demonstrated through simulations, a real system implementation and experiments
involving both static as well as mobile networks.
