Node Overlap Removal for 1D Graph Layout

Energy based algorithms are powerful techniques for laying out graphs. They tend to generate aesthetically pleasing graph embeddings, exhibiting symmetries and community structures. When dealing with large graphs, an important drawback of these algorithms is to produce embeddings where many nodes overlap, leading to cluttering issues. While several approaches have been proposed for node overlap removal on 2D graph layouts, to the best of our knowledge, there is no work dedicated to 1D graph layouts. In this paper, we first define 4 requirements for 1D graph node overlap removal. Then, we propose a O(|V|log(|V|)) time algorithm meeting these requirements. We illustrate our approach with two case studies based on arc diagrams where nodes are positioned by applying a MDS technique to highlight community structures. Finally, we compare our technique with alternatives from 2D graph techniques, and a discussion highlights some properties of the results.