Displacement Dynamic Bubble Charts

Bubble charts are often used to visualize numerical data associated with 2D data points: for every data point, a disc centered at the point has area that reflects its data value. When data points are geospatial locations, the visualization is a proportional symbol (circle) map. In a dynamic setting, data values change over time and can be shown using animation or small multiples. Bubble charts and proportional symbol maps suffer when overlapping discs obscure each other, making it difficult to estimate their sizes. We present an approach to remove or significantly reduce overlaps by allowing disc displacement while ensuring that each disc covers its location and that the east-west and north-south order of the discs is preserved. Specifically: (i) we minimize the number of overlapping pairs of discs or the sum of the widths of the overlaps, (ii) we minimize the sum of the distances of disc centers to their locations, and (iii) we minimize the sum of the movements of the discs over time. As even a simplified variant of the underlying problem is NP-hard, we propose solutions to several problem variants with efficiently-solvable quadratic-convex programming. We evaluate our approach on real-world data and compare the results to those obtained with a simpler force-directed approach. A functional prototype, as well as all source-code, datasets, and experiments, are available online.