A Note on the Complexity of One-Sided Crossing Minimization of Trees

TL;DR

This paper challenges a previous polynomial-time algorithm for one-sided crossing minimization in trees by providing a counterexample and proving the problem is NP-hard, indicating higher computational complexity than previously thought.

Contribution

The paper presents a counterexample to an existing polynomial-time algorithm and establishes NP-hardness for the problem, clarifying its true computational complexity.

Findings

Counterexample invalidates previous polynomial-time algorithm

Proves one-sided crossing minimization for trees is NP-hard

Reveals higher complexity than previously believed

Abstract

In 2011, Harrigan and Healy published a polynomial-time algorithm for one-sided crossing minimization for trees. We point out a counterexample to that algorithm, and show that one-sided crossing minimization is NP-hard for trees.