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Because of transient wireless link failures, incremental node deployment, and node mobility, existing information dissemination protocols used in wireless ad-hoc and sensor networks cause nodes to periodically broadcast "advertisement" containing the version of their current data item even in the "steady state" when no dissemination is being done. This is to ensure that all nodes in the network are up-to-date. This causes a continuous energy expenditure during the steady state, which is by far the dominant part of a network's lifetime. In this paper, we present a protocol called Varuna which incurs a constant energy cost, independent of the duration of the steady state. In Varuna, nodes monitor the traffic pattern of the neighboring nodes to decide when an advertisement is necessary. Using testbed experiments and simulations, we show that Varuna achieves several orders of magnitude energy savings compared to Trickle, the existing standard for dissemination in sensor networks, at the expense of a reasonable amount of memory for state maintenance.