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

This sharp decline from O(n1−a2d) to O(n1−a2d(lnnn)a2d) in the a-total movement of the sensors to attain complete coverage of the d-dimensional unit cube indicates the presence of an interesting threshold on the sensing radius in a d-dimensional unit cube as it increases from 12n1/d to 33/d(31/d−1)(31/d−1)12n1/d. In addition, we simulate Algorithm 2 and discuss the results of our simulations.