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

Abstract

The fundamental problem of energy-efficient reallocation of mobile random sensors to provide full coverage without interference is adressed in this paper.Consider n mobile sensors placed randomly in m−dimensional unit cube for fixed m ∈ {1, 2}. The sensors have identical sensing range, say r. We are interested in moving the sensors from their initial random positions to new locations so that every point in the unit cube is within the range of at least one sensor, while at the same time each pair of sensors is placed at interference distance greater or equal to s. Suppose the displacement of the i−th sensor is a distance d i . As a energy consumption for the displacement of a set of n sensors we consider the a−total displacement defined as the sum n i=1 d a i , for some constant a > 0. The main contribution of this paper can be summarized as follows.2 √ n and the interference distance equal to 1 √ n for the expected minimum a−total displacement.