On the displacement for covering a d-dimensional cube with randomly placed sensors

Consider n sensors placed randomly and independently with the uniform distribution in a d−dimensional unit cube (d ≥ 2). The sensors have identical sensing range equal to r, for some r > 0. We are interested in moving the sensors from their initial positions to new positions so as to ensure that the d−dimensional unit cube is completely covered, i.e., every point in the d−dimensional cube is within the range of a sensor. If the i-th sensor is displaced a distance di, what is a displacement of minimum cost that ensures coverage? As cost measure for the displacement of the team of sensors we consider the a-total movement defined as the sum Ma := n i=1 da i , for some constant a > 0. We assume that r and n are chosen so as to allow full coverage of the d−dimensional unit cube. Motivation for using this cost metric arises from the fact that there might be a terrain affecting the movement of the sensors from their initial to their final destinations (e.g., a terrain surfa...

• Type: Journal
• Year: 2016
• Where: ADHOC
• Authors: Rafal Kapelko, Evangelos Kranakis
• Keywords: ADHOC 2016, Database