  We present a 4-approximation algorithm for the problem of placing a fewest
guards on a 1.5D terrain so that every point of the terrain is seen by at least
one guard. This improves on the currently best approximation factor of 5. Our
method is based on rounding the linear programming relaxation of the
corresponding covering problem. Besides the simplicity of the analysis, which
mainly relies on decomposing the constraint matrix of the LP into totally
balanced matrices, our algorithm, unlike previous work, generalizes to the
weighted and partial versions of the basic problem.
