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The benefits of using mobile base station to prolong sensor network lifetime have been well recognized. However, due to the complexity of the problem (time-dependent network topology and traffic routing), theoretical performance limit and provably optimal algorithms remain difficult to develop. This paper fills this important gap by contributing theoretical results regarding the optimal movement of a mobile base station. Our main result hinges upon a novel transformation of the joint base station movement and flow routing problem from time domain to space domain. Based on this transformation, we first show that if the base station is allowed to be present only on a set of pre-defined points, then we can find the optimal time span for the base station on each of these points so that the overall network lifetime is maximized. Based on this finding, we show that when the location of the base station is un-constrained (i.e., can move to any point in the two-dimensional plane), we can develop an approximation algorithm for the joint mobile base station location and flow routing problem such that the network lifetime is guaranteed to be at least (1-epsiv) of the maximum network lifetime, where epsiv can be made arbitrarily small depending on required precision.