Level Planarity Is More Difficult Than We Thought

TL;DR

This paper demonstrates that existing quadratic time algorithms for the Level Planarity problem can produce incorrect results, indicating the problem's complexity is greater than previously believed.

Contribution

It provides counterexamples showing the limitations of three simple quadratic algorithms for Level Planarity, challenging prior assumptions about their correctness.

Findings

Counterexamples for existing algorithms

Algorithms can falsely reject level planarity

Algorithms can produce non-level planar drawings

Abstract

We consider three simple quadratic time algorithms for the problem Level Planarity and give a level-planar instance that they either falsely report as negative or for which they output a drawing that is not level planar.