Deriving Tidy Drawings of Trees

The tree-drawing problem is to produce a `tidy' mapping of elements of a tree to points in the plane. In this paper, we derive an eecient algorithm for producing tidy drawings of trees. The speciication, the starting point for the derivations, consists of a collection of intuitively appealing criteria satissed by tidy drawings. The derivation shows constructively that these criteria completely determine the drawing. Indeed, the criteria completely determine a simple but ineecient algorithm for drawing a tree, which can be transformed into an eecient algorithm using just standard techniques and a small number of inventive steps. The algorithm consists of an upwards accumulation followed by a downwards accumulation on the tree, and is further evidence of the utility of these two higher-order tree operations.