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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 reduction in energy consumption. To address this issue, we propose a novel data collection scheme, called the maximum amount shortest path (MASP), that increases network throughput as well as conserves energy to optimize the assignment of sensor nodes. MASP is formulated as an integer linear programming problem and then solved with the help of a genetic algorithm. A two-phase communication protocol is designed to implement the MASP scheme. Simulations experiments using OMNET++ show that MASP outperforms the shortest path tree (SPT) and static sink methods in terms of system throughput and energy efficiency.