Rafał Kapelko

Rafal Kapelko

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.

Rafal Kapelko

In this note we essentially simplify the proof of the main result in one paper from leading computer science conference 25th ACM Symposium on Parallelism in Algorithms and Architectures (see [3].) We also present direct method and give exact asymptotic result.

Sajal K. Das, Rafał Kapelko

This paper deals with random sensors initially randomly deployed on the line according to general random process and on the plane according to two independent general random processes. The mobile robot with carrying capacity $k$ placed at the origin point is to move the sensors to achieve the general scheduling requirement such as coverage, connectivity and thus to satisfy the desired communication property in the network. We study tradeoffs between the energy consumption in robot's movement, the numbers of sensors $n$, the sensor range $r$, the interference distance $s$, and the robot capacity $k$ until completion of the coverage simultaneously with interference scheduling task. In this work, we obtain upper bounds for the energy consumption in robot's movement and obtain the sharp decrease in the total movement cost of the robot so as to provide the coverage simultaneously with interference requirement.