Towards Low-Cost Yet High-Performance Sensor Networks by Deploying a Few Ultra-fast Charging Battery Powered Sensors

. 2018 Aug 23;18(9):2771. doi: 10.3390/s18092771

Algorithm 3 Algorithm for the routing allocation subproblem.

Input: a set $V_{s}$ of sensors, a set V of to-be-charged sensors, the residual energy $e_{i}$ of each sensor $v_{i}$ in $V_{s}$ at some time $t_{0}$ , the charging tour $C^{K}$ .

Output: routing $f_{i j}^{K}$ .

1:
Calculate the start charging time $t_{i}$ of each sensor $v_{i}$ in V by Constraint (7);
2:
Let $D_{l} = 0$ and $D_{u} = T$ ; /* $D_{l}$ and $D_{u}$ are the lower and upper bounds on the optimal value $D_{o p t}^{K}$ , respectively */
3:
while $D_{l} < D_{u}$ do
4:
Let $D_{g}^{K} = ⌊ \frac{D_{l} + D_{u}}{2} ⌋$ ; /* a guess of $D_{o p t}^{K}$ */
5:
if there are no feasible solutions $f_{i j}^{K}$ to LP $P_{4}$ then
6:
/* the guess $D_{g}^{K}$ is smaller than $D_{o p t}^{K}$ , i.e., $D_{g}^{K} < D_{o p t}^{K}$ */
7:
Let $D_{l} = D_{g}^{K} + 1$ ;
8:
else
9:
/* the guess $D_{g}^{K}$ is no less than $D_{o p t}^{K}$ , i.e., $D_{g}^{K} \geq D_{o p t}^{K}$ */
10:
Let $D_{u} = D_{g}^{K}$ ;
11:
end if
12:
end while
13:
Let $D_{o p t}^{K} = D_{u} (= D_{l})$ ;
14:
Find a feasible solution $f_{i j}^{K}$ to LP $P_{4}$ with $D_{o p t}^{K}$ ;
15:
return routing $f_{i j}^{K}$ .