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ZigBee, a unique communication standard designed for low-rate wireless personal area networks, has extremely low complexity, cost, and power consumption for wireless connectivity in inexpensive, portable, and mobile devices. Among the well-known ZigBee topologies, ZigBee cluster-tree is especially suitable for low-power and low-cost wireless sensor networks because it supports power saving operations and light-weight routing. In a constructed wireless sensor network, the information about some area of interest may require further investigation such that more traffic will be generated. However, the restricted routing of a ZigBee cluster-tree network may not be able to provide sufficient bandwidth for the increased traffic load, so the additional information may not be delivered successfully. In this paper, we present an adoptive-parent-based framework for a ZigBee cluster-tree network to increase bandwidth utilization without generating any extra message exchange. To optimize the throughput in the framework, we model the process as a vertex-constraint maximum flow problem, and develop a distributed algorithm that is fully compatible with the ZigBee standard. The optimality and convergence property of the algorithm are proved theoretically. Finally, the results of simulation experiments demonstrate the significant performance improvement achieved by the proposed framework and algorithm over existing approaches.