A Fast Successive Over-Relaxation Algorithm for Force-Directed Network Graph Drawing

TL;DR

This paper introduces a new SOR-based heuristic algorithm that guarantees convergence and significantly accelerates force-directed graph drawing, making it more practical for large-scale graphs.

Contribution

It provides a convergence condition and a novel SOR strategy to speed up force-directed algorithms, improving efficiency for large graphs.

Findings

Algorithm reduces iteration count and runtime significantly.

On average, the new method is 1.5 times faster than traditional approaches.

Computational tests confirm improved performance on benchmark datasets.

Abstract

Force-directed approach is one of the most widely used methods in graph drawing research. There are two main problems with the traditional force-directed algorithms. First, there is no mature theory to ensure the convergence of iteration sequence used in the algorithm and further, it is hard to estimate the rate of convergence even if the convergence is satisfied. Second, the running time cost is increased intolerablely in drawing large- scale graphs, and therefore the advantages of the force-directed approach are limited in practice. This paper is focused on these problems and presents a sufficient condition for ensuring the convergence of iterations. We then develop a practical heuristic algorithm for speeding up the iteration in force-directed approach using a successive over-relaxation (SOR) strategy. The results of computational tests on the several benchmark graph datasets used widely in graph drawing research show that our algorithm can dramatically improve the performance of force-directed approach by decreasing both the number of iterations and running time, and is 1.5 times faster than the latter on average.