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Low cost and low power consumption are two major design criteria in wireless sensor networks (WSN). To meet the increasing demand for localized fine-grained sensing with densely deployed WSNs, this paper proposes the use of a hybrid WSN that consists of nodes with standard transceivers and nodes with only transmitters. A two-phase Constrained-Scheduling based MAC protocol is proposed, which employs the "Automatic Resource Estimation (ARE)" method. Through analysis and extensive simulations, the proposed protocol is shown to achieve a significant performance improvement in terms of data delivery probability, QoS differentiation and energy minimization over existing MAC protocols for such networks. To the best of our knowledge, this work is the first effort to bring scheduling to WSNs that contains asynchronous and uncoordinated transmit-only nodes.