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Recent work shows that sink mobility along a constrained path can improve the energy efficiency in wireless sensor networks. However, due to the path constraint, a mobile sink with constant speed has limited communication time to collect data from the sensor nodes deployed randomly. This poses significant challenges in simultaneously improving the amount of data collected and prolonging network lifetime. To address this issue, we propose a optimal assignment of sensor nodes and routing solution, that maximize the network lifetime under the condition of maximizing the network throughput. Simulation experiments using OMNET++ show that our proposed scheme outperforms SPT and MASP in terms of total amount of data and network lifetime respectively.