  We investigate the interesting impact of mobility on the problem of efficient
wireless power transfer in ad hoc networks. We consider a set of mobile agents
(consuming energy to perform certain sensing and communication tasks), and a
single static charger (with finite energy) which can recharge the agents when
they get in its range. In particular, we focus on the problem of efficiently
computing the appropriate range of the charger with the goal of prolonging the
network lifetime. We first demonstrate (under the realistic assumption of fixed
energy supplies) the limitations of any fixed charging range and, therefore,
the need for (and power of) a dynamic selection of the charging range, by
adapting to the behavior of the mobile agents which is revealed in an online
manner. We investigate the complexity of optimizing the selection of such an
adaptive charging range, by showing that two simplified offline optimization
problems (closely related to the online one) are NP-hard. To effectively
address the involved performance trade-offs, we finally present a variety of
adaptive heuristics, assuming different levels of agent information regarding
their mobility and energy.
