Straight-Line Drawings of General Trees with Linear Area and Arbitrary Aspect Ratio

Trees are usually drawn planar, i.e. without any crossings. In this paper we investigate the area requirement of planar straight-line drawings of trees. A degree-d tree is one in which each node has at most d edges incident on it. Let T be a degree-d tree with n nodes, such that d = O(nδ), where δ < 1/2 is a constant. We show that T admits a planar straight-line grid drawing with area O(n) and with any prespecified aspect ratio in the range [1, nα], where α is a constant such that 0 ≤ α < 1. We also show that such a drawing can be constructed in O(n log n) time.