2017/08/31 by Thérèse Biedl, Biedl, Therese, Debajyoti Mondal +1
Computer Science · #Computational Geometry and Mesh Generation #Graph Theory and Algorithms #Computer Graphics and Visualization Techniques
paper · pdf · doi:10.48550/arxiv.1708.09515
Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known for straight-line drawings of trees under various restrictions such as edge length or slope constraints. On the other hand, there exist polynomial-time algorithms for computing minimum-width (resp., minimum-height) upward drawings of trees, where the height (resp., width) is unbounded. In this paper we take a major step in understanding the complexity of the area minimization problem for strictly-upward drawings of trees, which is one of the most common styles for drawing rooted trees. We prove that given a rooted tree T and a W× H grid, it is NP-hard to decide whether T admits a strictly-upward (unordered) drawing in the given grid.