Superlinear area conjecture for subtree-separated orthogonal drawings of complete ternary trees

Let $T$ be an $n$-node complete ternary tree. A planar straight-line orthogonal drawing of $T$ has the subtree separation property if the drawings of the subtrees rooted at distinct children of every node are separated as specified in the paper. Area is the area of the smallest axis-parallel enclosing rectangle of the drawing.

Superlinear area conjecture. There exists a constant $\varepsilon>0$ such that every $n$-node complete ternary tree requires

$$\Omega(n^{1+\varepsilon})$$

area in any planar straight-line orthogonal drawing satisfying the subtree separation property.

The conjecture is motivated by computational experiments on complete ternary trees and concerns a restricted class of drawings. The unrestricted asymptotic area requirements for ternary trees, and for complete ternary trees, remain open in the source.