Optimal Orthogonal Drawings of Triconnected Plane Graphs

In this paper we produce orthogonal drawings of triconnected planar graphs where a planar embedding is given. Kant presented an algorithm to compute a small orthogonal drawing in linear time. In this paper, we will show that his algorithm in fact produces less bends than the bound shown. Moreover, with a small variation of the algorithm, the number of bends can be reduced even further, which also leads to lower bounds on the grid-size. Both bounds are optimal.