A Greedy Heuristic for Crossing-Angle Maximization

TL;DR

This paper introduces a greedy heuristic algorithm for increasing crossing angles in graph drawings, which is effective and was recognized as the best in a 2017 challenge.

Contribution

It presents a simple, efficient heuristic for maximizing crossing angles in straight-line graph drawings, including a speed-up technique for crossing angle computation.

Findings

Heuristic effectively increases crossing angles in practice.

Algorithm outperformed competitors in the Graph Drawing Challenge 2017.

Speed-up technique improves computational efficiency.

Abstract

The crossing angle of a straight-line drawing $\Gamma$ of a graph $G=(V, E)$ is the smallest angle between two crossing edges in $\Gamma$. Deciding whether a graph $G$ has a straight-line drawing with a crossing angle of $90^\circ$ is $\mathcal NP$-hard. We propose a simple heuristic to compute a drawing with a large crossing angle. The heuristic greedily selects the best position for a single vertex in a random set of points. The algorithm is accompanied by a speed-up technique to compute the crossing angle of a straight-line drawing. We show the effectiveness of the heuristic in an extensive empirical evaluation. Our heuristic was clearly the winning algorithm (CoffeeVM) in the Graph Drawing Challenge 2017.