Rectangular grid drawings of plane graphs

The rectangular grid drawing of a plane graph G is a drawing of G such that each vertex is located on a grid point, each edge is drawn as a horizontal or vertical line segment, and the contour of each face is drawn as a rectangle. In this paper we give a simple linear-time algorithm to find a rectangular grid drawing of G if it exists. We also give an upper bound \(W + H \leqslant \frac{n}{2}\)on the sum of required width W and height H and a bound \(W + H \leqslant \frac{{n^2 }}{{16}}\)on the area of a rectangular grid drawing of G, where n is the number of vertices in G. These bounds are best possible, and hold for any compact rectangular grid drawing.