Lower bounds and parallel algorithms for planar orthogonal grid drawings

The paper considers the problem of constructing a planer orthogonal grid drawing (or more simply, layout) of an n-vertex graph, with the goal of minimizing the number of bends along the edges. It exhibits graphs that require Ω(n) bends in any layout, and shows that there exist optimal drawings that require Ω(n) bends and have all of them on a single edge of length Ω(n²). On the other side of the coin, it presents a parallel algorithm that runs on a CREW PRAM in O(log n) time with n/log n processors and constructs layouts with O(n) maximum edge length and O(n²) area. for biconnected graphs the number of bends is at most 2n+4, which is optimal in the worst-case. This work finds applications in VLSI layout, aesthetic graph drawing, and communication by light or microwave