Straight-line Orthogonal Drawing of Complete Ternary Tree Requires $O(n^{1.032})$ Area

TL;DR

This paper proves tight bounds on the minimal area for straight-line orthogonal drawings of complete ternary trees, showing it grows roughly as n^{1.031} to n^{1.032}, resolving a longstanding conjecture.

Contribution

It establishes the first tight asymptotic bounds on the minimal drawing area for complete ternary trees under the subtree separation property.

Findings

Lower bound of Ω(n^{1.031}) on drawing area

Upper bound of O(n^{1.032}) on drawing area

Resolution of a conjecture on minimal area requirements

Abstract

We resolve a conjecture posed by Covella, Frati and Patrignani by proving the straight-line orthogonal drawing of the complete ternary tree with $n$ nodes satisfying the subtree separation property with smallest area has area $\Omega(n^{1.031})$. We also improve the upper bound of this area to $O(n^{1.032})$.