Minimizing the area for planar straight-line grid drawings

Abstract

Straight-line grid drawings of bounded size is a classical topic in graph drawing. The Graph Drawing Challenge 2006 dealt with minimizing the area of planar straight-line grid drawings. In this paper, we show that it is NP-complete to decide if a planar graph has a planar straight-line drawing on a grid of given size. Furthermore, we present a new iterative approach to compactify planar straight-line grid drawings. In an experimental study, we evaluate the quality of the compactified drawings with respect to the size of the area as well as to other measures. © 2008 Springer-Verlag Berlin Heidelberg.