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Recent years have witnessed the emergence of numerous new Internet services for mobile users. Supporting mobile applications through public Wi-Fi networks has received significant research attention. Nevertheless, recent empirical studies have shown that unplanned Wi-Fi networks cannot provide satisfactory quality of service (QoS) for interactive mobile applications because of intermittent network connectivity. In this paper, we exploit statistical mobility characteristics of users to deploy Wi-Fi Access Points (APs) for continuous service for mobile users. We study two AP deployment problems that aim at maximizing the continuous user coverage and minimizing the AP deployment cost, respectively. Both problems are formulated based on mobility graphs that capture the statistical mobility patterns of users. We prove that both problems are not only NP-complete but are identical to each other as well. We develop several optimal and approximation algorithms for different topologies of mobility graphs. We prove that our approximation algorithms generate the result that is at least half of the optimal solution. The effectiveness of our approaches is validated by extensive simulations using real user mobility traces.