Analysis of the Threshold for Energy Consumption in Displacement of Random Sensors

. 2022 Nov 14;22(22):8789. doi: 10.3390/s22228789

Algorithm 1

M V (n, ρ, s)

moving sensors on

[0, 1]

Require: The initial locations of n mobile sensors, placed uniformly and independently at random on the unit interval $[0, 1]$ .

Ensure: The final positions of the sensors such that:

(i)
The distance between consecutive sensors is greater than or equal to s and less than or equal to $ρ .$
(ii)
The leftmost sensor is at a distance less than or equal to $\frac{ρ}{2}$ from the origin.

Initialization: Sort the initial locations of n sensors with respect to the origin of the interval, the location of sensors after sorting

X_{(1)} \leq X_{(2)} \leq \dots \leq X_{(n)};

1:
Let $X_{0} = 0;$
2:
for $i = 1$ ndo
3:
if $X_{(i)} - X_{(i - 1)} < s$ then
4:
move left to right the sensor $X_{(i)}$ to the new position $min (s + X_{(i - 1)}, 1);$
5:
else if $X_{(i)} - X_{(i - 1)} > ρ$ then
6:
move right to left the sensor $X_{(i)}$ to the new position $ρ + X_{(i - 1)};$
7:
else
8:
do nothing;
9:
end if
10:
end for
11:
if $X_{(1)} > \frac{1}{2} ρ$ then
12:
$z : = X_{(1)} - \frac{1}{2} ρ;$
13:
for $i = 1$ n do
14:
move right to left the sensor $X_{(i)}$ to the new position $X_{(i)} - z;$
15:
end for
16:
end if