# On the Area Requirements of Planar Straight-Line Orthogonal Drawings of Ternary Trees

## TL;DR

This paper investigates the area needed for planar straight-line orthogonal drawings of ternary trees, proving sub-quadratic bounds, providing experimental results, and establishing lower bounds on side lengths.

## Contribution

It establishes sub-quadratic area bounds for all ternary trees and introduces new bounds and conjectures for complete ternary trees.

## Key findings

- Every ternary tree admits a planar orthogonal drawing in sub-quadratic area.
- Experimental evaluation supports the proposed bounds.
- A polynomial lower bound on the minimum side length of such drawings is presented.

## Abstract

In this paper, we study the area requirements of planar straight-line orthogonal drawings of ternary trees. We prove that every ternary tree admits such a drawing in sub-quadratic area. Further, we present upper bounds, the outcomes of an experimental evaluation, and a conjecture on the area requirements of planar straight-line orthogonal drawings of complete ternary trees. Finally, we present a polynomial lower bound on the length of the minimum side of any planar straight-line orthogonal drawing of a complete ternary tree.