An effective crossing minimisation heuristic based on star insertion

TL;DR

This paper introduces a new heuristic for graph crossing minimization that repeatedly solves the star insertion problem, demonstrating effectiveness especially for dense graphs through experimental validation.

Contribution

The paper presents a novel heuristic based on star insertion for crossing minimization, with practical implementation details and experimental comparison to existing methods.

Findings

Performs well on dense graph instances

Compared favorably to existing crossing minimization methods

Effective in practical scenarios

Abstract

We present a new heuristic method for minimising crossings in a graph. The method is based upon repeatedly solving the so-called {\em star insertion problem} in the setting where the combinatorial embedding is fixed, and has several desirable characteristics for practical use. We introduce the method, discuss some aspects of algorithm design for our implementation, and provide some experimental results. The results indicate that our method compares well to existing methods, and also that it is suitable for dense instances.