  In this paper we focus on the mobile sensor coverage problem formulated as a
continuous locational optimization problem. Cort\`es et al. first proposed a
distributed version of the Lloyd descent algorithm with guaranteed convergence
to a local optima. Since then researchers have studied a number of variations
of the coverage problem. The quality of the final solution with the Lloyd
descent depends on the initial sensor configuration. Inspired by the recent
results on a related $k$-means problem, in this paper we propose the
weighted-$D^2$ sampling to choose the initial sensor configuration and show
that it yields $O(\log k)$-competitive sensor coverage before even applying the
Lloyd descent. Through extensive numerical simulations, we show that the
initial coverage with the weighted-$D^2$ sampling is significantly lower than
that with the uniform random initial sensor configuration. We also show that
the average distance traveled by the sensors to reach the final configuration
through the Lloyd descent is also significantly lower than that with the
uniform random configuration. This also implies considerable savings in the
energy spent by the sensors during motion and faster convergence.
