Tiling a polygon with parallelograms (Q2366227)

The author devises a quadratic time algorithm determining if a simple polygon admits a tiling by parallelograms, and if so constructing it. It is also shown that the problem is of the same complexity if the tiles must be picked from a fixed set of parallelograms. Three generalizations of the problem (tiling a polygon by a fixed set of triangles or trapezoids, tiling polgyons with holes by parallelograms) are shown to be \(NP\)-complete.