Efficient Drawing Algorithms on the Minimum Area for Tree-Structured Diagrams

In this paper, we deal with a treelike diagram which we call a”tree structured $\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{m}$” $(TSD$ for short). A $TSD$ is a generalization of program diagrams. We firstly define the problem of drawing TSDs and introduce constraints for beautiful drawings of TSDS. Then we present efficient $O(n)$ and $O(n^{2})$ algorithms which produces minimum width drawing unders certain sets of constraints. These algorithms will be applied to practical uses such as visual programming and others.