Analysis of the Threshold for Energy Consumption in Displacement of Random Sensors
This work provides theoretical insights into the fundamental limits of sensor displacement for coverage, relevant to wireless sensor network design.
The paper analyzes the energy-efficient reallocation of mobile random sensors to achieve full coverage without interference, identifying sharp thresholds in expected minimal total displacement at specific sensing radii and interference distances for both unit interval and unit square placements.
The fundamental problem of energy-efficient reallocation of mobile random sensors to provide full coverage without interference is addressed in this paper. We consider $n$ mobile sensors with identical sensing range placed randomly on the unit interval and on the unit square. The main contribution is summarized as follows: If the sensors are placed on the unit interval we explain the sharp increase around the sensing radius equal to $\frac{1}{2n}$ and the interference distance equal to $\frac{1}{n}$ for the expected minimal $a$-total displacement, If the sensors are placed on the unit square we explain the sharp increase around the square sensing radius equal to $\frac{1}{2 \sqrt{n}}$ and the interference distance equal to $\frac{1}{\sqrt{n}}$ for the expected minimal $a$-total displacement.