This paper presents a graph bundling algorithm that agglomerates edges taking into account both spatial proximity as well as user-defined criteria in order to reveal patterns that were not perceivable with previous bundling techniques. Each edge belongs to a group that may either be an input of the problem or found by clustering one or more edge properties such as origin, destination, orientation, length or domain-specific properties. Bundling is driven by a stack of density maps, with each map capturing both the edge density of a given group as well as interactions with edges from other groups. Density maps are efficiently calculated by smoothing 2D histograms of edge occurrence using repeated averaging filters based on integral images. A CPU implementation of the algorithm is tested on several graphs, and different grouping criteria are used to illustrate how the proposed technique can render different visualizations of the same data. Bundling performance is much higher than on previous approaches, being particularly noticeable on large graphs, with millions of edges being bundled in seconds.
In 2011, proposed a multilevel agglomerative edge bundling method (MINGLE) based on minimizing the ink needed to represent edges, with additional constraints on the curvature of the resulting splines @cite_16 . While drawings are more cluttered and less smooth than some of the previous techniques, MINGLE remains the fastest algorithm and the only that demonstrated being able to coupe with graphs comprised by millions of edges, although requiring several minutes to process them. proposed Ordered Bundles (OB) @cite_8 , where edge routing is accomplished through a heuristic that tries to minimize the total length of the paths together with their ink. After bundling, the method separates edges belonging to the same bundle to allow detailed local views. Computing times are higher than several of the previous approaches but, in the other hand, this technique offers a level of detail not previously achieved.
@cite_16 @cite_8
1982799219 1793674997
Graphs are often used to encapsulate relationships between objects. Node-link diagrams, commonly used to visualize graphs, suffer from visual clutter on large graphs. Edge bundling is an effective technique for alleviating clutter and revealing high-level edge patterns. Previous methods for general graph layouts either require a control mesh to guide the bundling process, which can introduce high variation in curvature along the bundles, or all-to-all force and compatibility calculations, which is not scalable. We propose a multilevel agglomerative edge bundling method based on a principled approach of minimizing ink needed to represent edges, with additional constraints on the curvature of the resulting splines. The proposed method is much faster than previous ones, able to bundle hundreds of thousands of edges in seconds, and one million edges in a few minutes. We propose a new approach to edge bundling. At the first stage we route the edge paths so as to minimize a weighted sum of the total length of the paths together with their ink. As this problem is NP-hard, we provide an efficient heuristic that finds an approximate solution. The second stage then separates edges belonging to the same bundle. To achieve this, we provide a new and efficient algorithm that solves a variant of the metro-line crossing minimization problem. The method creates aesthetically pleasing edge routes that give an overview of the global graph structure, while still drawing each edge separately, without intersecting graph nodes, and with few crossings.