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Recent advances have shown a great potential of mobile data gathering in wireless sensor networks, where one or more mobile collectors are employed to collect data from sensors via short-range communications. Among a variety of data gathering approaches, one typical scheme is called anchor-based mobile data gathering. In such a scheme, during each periodic data gathering tour, the mobile collector stays at each anchor point for a period of sojourn time, and in the meanwhile the nearby sensors transmit data to the collector in a multihop fashion. In this paper, we focus on such a data gathering scheme and provide distributed algorithms to achieve its optimal performance. We consider two different cases depending on whether the mobile collector has fixed or variable sojourn time at each anchor point. We adopt network utility, which is a properly defined function, to characterize the data gathering performance, and formalize the problems as network utility maximization problems under the constraints of guaranteed network lifetime and data gathering latency. To efficiently solve these problems, we decompose each of them into several subproblems and solve them in a distributed manner, which facilitates the scalable implementation of the optimization algorithms. Finally, we provide extensive numerical results to demonstrate the usage and efficiency of the proposed algorithms and complement our theoretical analysis.