Area Minimization for Grid Visibility Representation of Hierarchically Planar Graphs

Abstract. Hierarchical graphs are an important class of graphs for modelling many real applications in software and information visualization. In this paper, we shall investigate the computational complexity of constructing minimum area grid visibility representations of hierarchically planar graphs. Firstly, we provide a quadratic algorithm that minimizes the drawing area with respect to a fixed planar embedding. This implies that the area minimization problem is polynomial time solvable restricted to the class of graphs whose planar embeddings are unique. Secondly, we show that the area minimization problem is generally NP-hard.

• Type: Conference
• Year: 1999
• Where: COCOON
• Authors: Xuemin Lin, Peter Eades
• Keywords: Area Minimization Problem, COCOON 1999, Combinatorics, Planar Embeddings, Planar Graphs