Planar grid embedding in linear time

The authors consider the problem of constructing a planar grid embedding for G, where G is a planar graph with n vertices, which maps vertices to distinct grid points and edges to nonintersecting grid paths. A new algorithm is presented that runs in O( n) time and produces grid embeddings with the following properties: (1) the total number of bends is at most 2.4n+2; (2) the number of bends along each edge is at most 4; (3) the length of every edge is O(n); and (4) the area of the embedding is O(n²)