Optimal orthogonal drawings of Triconnected plane graphs

Abstract

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. We also present a theorem that gives a bound on the grid-size of an orthogonal drawing, assuming that a bound on the number of bends is known. With the help of this theorem, we can prove bounds on the gridsize for the algorithm of Tamassla, which produces the minimum number of bends. No such bounds were known before.