  We revisit the static coverage control problem for placement of vehicles with
simple motion on the real line, under the assumption that the cost is a
polynomial function of the locations of the vehicles. The main contribution of
this paper is to demonstrate the use of tools from numerical algebraic
geometry, in particular, a numerical polynomial homotopy continuation method
that guarantees to find all solutions of polynomial equations, in order to
characterize the \emph{global minima} for the coverage control problem. The
results are then compared against a classic distributed approach involving the
use of Lloyd descent, which is known to converge only to a local minimum under
certain technical conditions.
