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This paper proposes a novel energy saving scheme, termed the Gossip-based sleep protocol (GSP). With GSP, each node randomly goes to sleep for some time with gossip sleep probability p. When the value of p is small enough, the network stays connected. GSP does not require a wireless node to maintain the states of other nodes. It requires few operations and scales to large networks. Two versions of GSP, one for synchronous networks and one for asynchronous networks are proposed, and the advantages of the GSP approach through both simulations and analysis is showed in this paper.