  An obstacle representation of a plane graph G is V(G) together with a set of
opaque polygonal obstacles such that G is the visibility graph on V(G)
determined by the obstacles. We investigate the problem of computing an
obstacle representation of a plane graph (ORPG) with a minimum number of
obstacles. We call this minimum size the obstacle number of G.
  First, we show that ORPG is NP-hard by reduction from planar vertex cover,
resolving a question posed by [8]. Second, we give a reduction from ORPG to
maximum degree 3 planar vertex cover. Since this reduction preserves solution
values, it follows that ORPG is fixed parameter tractable (FPT) and admits a
polynomial-time approximation scheme (PTAS).
