Straight-line Drawings of Binary Trees with Linear Area and Arbitrary Aspect Ratio

Straight-line Drawings of Binary Trees with Linear Area and Arbitrary Aspect Ratio

Trees are usually drawn planar, i.e. without any edge-crossings. In this paper, we investigate the area requirement of (non-upward) planar straight-line grid drawings of binary trees. Let T be a binary tree with n nodes. We show that T admits a planar straight-line grid drawing with area O(n) and with any pre-specified aspect ratio in the range [n− , n ], where is any constant, such that 0 < < ...

Straight-line Drawings of Binary Trees with Linear Area and Good Aspe t Ratio

Optimizing Area and Aspect Ratio in Straight-Line Orthogonal Tree Drawings

We investigate the problem of drawing an arbitrary n-node binary tree orthogonally in an integer grid using straight-line edges. We show that one can simultaneously achieve good area bounds while also allowing the aspect ratio to be chosen as being O(1) or sometimes even an arbitrary parameter. In addition, we show that one can also achieve an additional desirable aesthetic criterion, which we ...

3D Straight-line Drawings of k-trees

This paper studies the problem of computing 3D crossing-free straight-line grid drawings of graphs such that the overall volume is small. We show that every 2-tree (and therefore every series-parallel graph) can be drawn on an integer 3D grid consisting of 15 parallel lines and having linear volume. We extend the study to the problem of drawing general k-trees on a set of parallel grid lines. L...

LR-Drawings of Ordered Rooted Binary Trees and Near-Linear Area Drawings of Outerplanar Graphs

We study a family of algorithms, introduced by Chan [SODA 1999], for drawing ordered rooted binary trees. Any algorithm in this family (which we name an LR-algorithm) takes in input an ordered rooted binary tree T with a root rT , and recursively constructs drawings ΓL of the left subtree L of rT and ΓR of the right subtree R of rT ; then either it applies the left rule, i.e., it places ΓL one ...