O(n) and O(n2) Time Algorithms for Drawing Problems of Tree-Structured Diagrams

We investigate sets of conditions with respect to narrower drawing of tree-structured diagrams on an integral lattice. We found that under certain sets of conditions there are practical procedural algorithms for narrower drawing of tree-structured diagrams, while under other sets of conditions there are none. Based on our findings, we present efficient algorithms that provide narrower placement satisfying given amorphous conditions. In intractable conditions, we propose a constraint-based algorithm for drawing tree-structured diagrams with a minimum-width by limiting the number of cells. Our results provide a criterion for deciding under given conditions, whether to use procedural or constraint-based algorithms to draw a tree-structured diagram.