This paper studies local-control strategies to estimate the size of a certain event affecting an arbitrary connected subset of nodes in a network. For example, our algorithms allow nodes in a peer-to-peer system to explore the remaining connected components after a Denial-ofService attack, or nodes in a sensor network to assess the magnitude of a certain environmental event. In our model, each node can keep some extra information about its neighborhood computed during the deployment phase of the network. On the arrival of the event, the goal of the active nodes is to learn the network topology induced by the event, without the help of the remaining nodes. This paper studies the tradeoffs between message and time complexity of possible distributed solutions.

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