Node overlap removal is a necessary step in many scenarios including laying out a graph, or visualizing a tag cloud. Our contribution is a new overlap removal algorithm that iteratively builds a Minimum Spanning Tree on a Delaunay triangulation of the node centers and removes the node overlaps by "growing" the tree. The algorithm is simple to implement yet produces high quality layouts. According to our experiments it runs several times faster than the current state-of-the-art methods.
There is vast research on node overlap removal. Some methods, including hierarchical layouts , incorporate the overlap removal with the layout step. Likewise, force-directed methods have been extended to take the node sizes into account , but it is difficult to guarantee overlap-free layouts without increasing the repulsive forces extensively. @cite_4 show how to avoid node overlaps with Stress Majorization . The method can remove node overlaps during the layout step, but it needs an initial state that is overlap free; sometimes such a state is not given.
@cite_4
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The problem of node overlap removal is to adjust the layout generated by typical graph drawing methods so that nodes of non-zero width and height do not overlap, yet are as close as possible to their original positions. We give an O(n log n) algorithm for achieving this assuming that the number of nodes overlapping any single node is bounded by some constant. This method has two parts, a constraint generation algorithm which generates a linear number of “separation” constraints and an algorithm for finding a solution to these constraints “close” to the original node placement values. We also extend our constraint solving algorithm to give an active set based algorithm which is guaranteed to find the optimal solution but which has considerably worse theoretical complexity. We compare our method with convex quadratic optimization and force scan approaches and find that it is faster than either, gives results of better quality than force scan methods and similar quality to the quadratic optimisation approach. When drawing graphs whose nodes contain text or graphics, the nontrivial node sizes must be taken into account, either as partof the initial layout or as a post-processing step. The core problem in avoiding or removing overlaps is to retain the structural information inherent in a layout while minimizing the additional area required. Thispaper presents a new node overlap removal algorithm that does well at retaining a graph’s shape while using little additional area and time. As part ofthe analysis, we consider and evaluate two measures of dissimilarity for two layouts of the same graph. Techniques for drawing graphs have proven successful in producing good layouts of undirected graphs. When nodes must be labeled however, the problem of overlapping nodes arises, particularly in dynamic graph visualization. Providing a formal description of this problem, this paper presents a new approach called the Force-Transfer algorithm that removes node overlaps. Compared to other methods, our algorithm is usually able to achieve a compact adjusted layout within a reasonable running time. We present the H3 layout technique for drawing large directed graphs as node-link diagrams in 3D hyperbolic space. We can lay out much larger structures than can be handled using traditional techniques for drawing general graphs because we assume a hierarchical nature of the data. We impose a hierarchy on the graph by using domain-specific knowledge to find an appropriate spanning tree. Links which are not part of the spanning tree do not influence the layout but can be selectively drawn by user request. The volume of hyperbolic 3-space increases exponentially, as opposed to the familiar geometric increase of euclidean 3-space. We exploit this exponential amount of room by computing the layout according to the hyperbolic metric. We optimize the cone tree layout algorithm for 3D hyperbolic space by placing children on a hemisphere around the cone mouth instead of on its perimeter. Hyperbolic navigation affords a Focus+Context view of the structure with minimal visual clutter. We have successfully laid out hierarchies of over 20,000 nodes. Our implementation accommodates navigation through graphs too large to be rendered interactively by allowing the user to explicitly prune or expand subtrees.