On the k-weak Coverage of Random Mobile Sensors

This paper studies the fundamental problem of energy consumption in the movement of mobile random sensors ensuring k-weak coverage on the domain. In particular, we analyze two notions of k-weak coverage on the unit square, namely (1) $(k, x)$-weak coverage in which every straight-line path across the width of the unit square passes through the sensing range of at least k sensors; and (2) $(k, x, y)$-weak coverage in which every straight-line path across the width and the length of the unit square passes through the sensing range of at least k sensors. The number of reliable and p-reliable sensors (i.e., each sensor is reliable with probability p independently from other sensors) in energy-efficient reallocation is optimized to provide the desired k-weak coverage. For reliable sensors, we discover sharp decrease in the expected minimal energy consumption in the movement to provide the desired k-weak coverage as a function of the number of sensors. For p-reliable sensors, we design and analyze two energy-efficient algorithms to ensure the k-weak coverage. The novelty of the paper is in the theoretical understanding and analysis.