Usage of mobile sink(s) for data gathering in wireless sensor networks(WSNs) improves the performance of WSNs in many respects such as power consumption, lifetime, etc. In some applications, the mobile sink $MS$ travels along a predefined path to collect data from the nearby sensors, which are referred as sub-sinks. Due to the slow speed of the $MS$, the data delivery latency is high. However, optimizing the {\em data gathering schedule}, i.e. optimizing the transmission schedule of the sub-sinks to the $MS$ and the movement speed of the $MS$ can reduce data gathering latency. We formulate two novel optimization problems for data gathering in minimum time. The first problem determines an optimal data gathering schedule of the $MS$ by controlling the data transmission schedule and the speed of the $MS$, where the data availabilities of the sub-sinks are given. The second problem generalizes the first, where the data availabilities of the sub-sinks are unknown. Plane sweep algorithms are proposed for finding optimal data gathering schedule and data availabilities of the sub-sinks. The performances of the proposed algorithms are evaluated through simulations. The simulation results reveal that the optimal distribution of data among the sub-sinks together with optimal data gathering schedule improves the data gathering time.