Fault-Tolerant Wireless Charger Placement

In many real-life applications, wireless chargers are deployed outdoor or in public area or even unattended environment such as hotels, restaurants, retail stores. They are exposed to various risks and malicious attacks that may break them down and further incur significant cost (e.g., battery replacement and maintenance) or performance degradation. Hence, we consider the problem of
F
ault-tolerant w
I
reless cha
R
ger place
M
ent (FIRM): given a set of wireless chargers and a set of tasks to be collaboratively conducted by a set of rechargeable devices, determining where to deploy the chargers to maximize the worst-cast overall task charging utility subject to the constraint that up to
$\tau$
chargers may break down. FIRM is a non-linear combinatorial two-level optimization problem. We first consider a relaxed version of FIRM (FIRM-R for short) corresponding to the inner optimization problem in FIRM. To address FIRM-R, we first propose an area discretization scheme to convert the infinite solution space into finite candidate positions. We then devise a power allocation method, based on which we prove that FIRM-R falls into the realm of maximizing a monotone submodular function under a uniform constraint. We then propose a constant-factor approximation algorithm to solve FIRM-R. Taking the above approximation algorithm as a subroutine, we further develop an approximation algorithm that solves FIRM with a constant-factor approximation ratio. Our extensive simulations and field experiments demonstrate that the overall charging utility of our proposed algorithm FIRM considering fault tolerance by greedy removal of
$\tau$
chargers outperforms the that of FIRM-R without considering fault tolerance by greedy removal of
$\tau$
chargers by at least
$119.89\%$
.