The Straight-Line RAC Drawing Problem is NP-Hard

TL;DR

This paper proves that determining whether a graph can be drawn with straight lines intersecting at right angles (RAC drawings) is an NP-hard problem, using a specific class of graphs with unique RAC embeddings.

Contribution

The paper introduces a class of graphs with unique RAC embeddings and proves the NP-hardness of deciding RAC drawings for these graphs.

Findings

Deciding RAC drawings is NP-hard.

A specific class of graphs with unique RAC embeddings is constructed.

The result links cognitive experiments to computational complexity.

Abstract

Recent cognitive experiments have shown that the negative impact of an edge crossing on the human understanding of a graph drawing, tends to be eliminated in the case where the crossing angles are greater than 70 degrees. This motivated the study of RAC drawings, in which every pair of crossing edges intersects at right angle. In this work, we demonstrate a class of graphs with unique RAC combinatorial embedding and we employ members of this class in order to show that it is NP-hard to decide whether a graph admits a straight-line RAC drawing.