Smartphones now become an indispensable part of our daily life. However, maintaining a smartphone's continuing operation consumes lots of battery energy. For example, a fully-charged smartphone usually cannot support its continuing operation for a whole day. A fundamental issue on a smartphone is its energy issue. That is, how to prolong the lifetime of a smartphone so that it can run as long as possible to meet its user needs. Wireless energy transfer has been demonstrated as a promising technique to address this issue. In this paper, we study a novel smartphone charging problem, through wireless chargers deployed on public commuters, e.g., subway trains, to charge energy-critical smartphones when their users take subway trains to work or go home. Since the amounts of residual energy of different smartphones are significantly different, the charging satisfactions of different users are essentially different. In this paper, we formulate this charging satisfaction problem as a novel optimization problem that schedules the limited number of wireless chargers on subway trains to charge energy-critical smartphones such that the overall charging satisfaction of smartphone users is maximized, for a given monitoring period (e.g., one day). Forthis problem, we first devise a 1/3-approximation algorithm if the travel trajectory of each smartphone user is given. We then propose an online algorithm to deal with dynamic energy-critical smartphone charging requests. We also propose a nontrivial distributed scheduling algorithm for a variant of the problem where the global knowledge of user energy information is unknown. We finally evaluate the performance of the proposed algorithms through experimental simulations, using a real dataset of subway-taking in San Francisco. The experimental results show that the proposed algorithms are very promising, and over 90 percent of energy-critical user smartphones can be satisfactorily charged in a one-day monitoring period.
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