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We consider decentralized binary detection in a sensor network. The tradeoff between detection reliability and resource utilization plays an important role in such a network, due to the limited availability of resources such as energy. Censoring, whereby the network chooses some sensors to make observations and puts others to 'sleep', is one approach for managing this tradeoff. We allow general censoring strategies, based on side information available at each sensor, and assume that all side information is shared throughout the network, thus allowing cooperation in making censoring decisions. We obtain the rather surprising result that such cooperation is unnecessary in the asymptotic regime of a large network and a small Type I error. We also provide a censoring strategy that achieves asymptotically optimal performance.