On the approximability of two tree drawing conventions

We consider two aesthetic criteria for the visualization of rooted trees: inclusion and tip-over. Finding the minimum area layout according to either of these two standards is an NP-hard task, even when we restrict ourselves to binary trees. We provide a fully polynomial time approximation scheme for this problem. This result applies to any tree for tip-over layouts and to bounded degree trees in the case of the inclusion convention. We also prove that such restriction is necessary since, for unbounded degree trees, the inclusion problem is strongly NP-hard. Hence, neither a fully polynomial time approximation scheme nor a pseudopolynomial time algorithm exists, unless P = NP. Our technique, combined with the parallel algorithm by Metaxas et al. [Comput. Geom. 9 (1998) 145

• Type: Journal
• Year: 2002
• Where: IPL
• Authors: Paolo Penna
• Keywords: Degree Trees, Fully Polynomial Time Approximation Scheme, IPL 2002, Unbounded Degree Trees