On planar polyline drawings

Abstract

We present a linear time algorithm that produces a planar polyline drawing for a plane graph with n vertices in a grid of size bounded by (p∈+∈1) ×(n∈-∈2), where . It uses at most bends, and each edge uses at most one bend. Compared with the area optimal polyline drawing algorithm in [3], our algorithm uses a larger grid size bound in trade for a smaller bound on the total number of bends. Their bend bound is (n∈-∈2). Our algorithm is based on a transformation from Schnyder's realizers [6,7] of maximal plane graphs to transversal structures [4,5] for maximal internally 4-connected plane graphs. This transformation reveals important relations between the two combinatorial structures for plane graphs, which is of independent interest. © 2008 Springer-Verlag Berlin Heidelberg.