Optimizing area and aspect ratio in straight-line orthogonal tree drawings

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 ...

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 < < ...

Area-eecient Algorithms for Upward Straight-line Tree Drawings ?

In this paper, we investigate planar upward straight-line grid drawing problems for bounded-degree rooted trees so that a drawing takes up as little area as possible. A planar upward straight-line grid tree drawing satisses the following four constraints: (1) all vertices are placed at distinct grid points (grid), (2) all edges are drawn as straight lines (straight-line), (3) no two edges in th...

Straight Line Orthogonal Drawings of Complete Ternery Trees

In this paper we study embeddings of complete ternary trees in a 2-D lattice. Suppose we are given an n-node complete ternary tree Tn with height h. We can construct an embedding of Th on a 2-D lattice L so that every node in Th corresponds to a vertex in L, and every edge in Th corresponds to a horizontal or vertical path in the lattice. We provide a better upper bound on the area requirement ...

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