A linear algorithm for 2-bend embeddings of planar graphs in the two-dimensional grid Original Research Article

In this paper we describe a linear algorithm for embedding planar graphs in the rectilinear two-dimensional grid, where vertices are grid points and edges are noncrossing grid paths. The main feature of our algorithm is that each edge is guaranteed to have at most 2 bends (with the single exception of the octahedron for which 3 bends are needed). The total number of bends is at most2n + 4 if the graph is biconnected and at most(7/3)n in the general case. The area is(n + 1)2 in the worst case. This problem has several applications to VLSI circuit design, aesthetic layout of diagrams, computational geometry.