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In wireless sensor networks, efficiently disseminating data from a dynamic source to multiple mobile sinks is important for applications such as mobile target detection and tracking. A tree-based multicasting scheme can be used. However, due to the short communication range of each sensor node and the frequent movement of sources and sinks, a sink may fail to receive data due to broken paths, and the tree should frequently be reconfigured to reconnect sources and sinks. To address the problem, we propose a dynamic proxy tree-based framework. A big challenge in implementing the framework is how to reconfigure the proxy tree efficiently as sources and sinks change. We model the problem as on-line construction of a minimum Steiner tree in a Euclidean plane, and propose centralized schemes to solve it. Considering the strict energy constraints in wireless sensor networks, we further propose two distributed on-line schemes, a shortest path-based (SP) scheme and a spanning range-based (SR) scheme. Extensive simulations are conducted to evaluate the schemes. The results show that the distributed schemes have similar performance to the centralized ones, and among the distributed schemes, SR outperforms SP.