  In this paper, we consider the problem of covering a plane region with unit
discs. We present an improved upper bound and the first nontrivial lower bound
on the number of discs needed for such a covering, depending on the area and
perimeter of the region. We provide algorithms for efficient covering of convex
polygonal regions using unit discs. We show that the computational complexity
of the algorithms is pseudo-polynomial in the size of the input and the output.
We also show that these algorithms provide a constant factor approximation of
the optimal covering of the region.
