Graph Drawing by Stress Majorization

Gansner, Emden R.; Koren, Yehuda; North, Stephen C.

doi:10.1007/978-3-540-31843-9_25

Cited by 303 publications

(275 citation statements)

References 16 publications

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“…For each graph and edge embeddedness method, we iteratively increase the sparsification ratio by 10% and compute the corresponding backbone. Layouts are computed using stress majorization [9] initialized by PivotMDS [3] as suggested in [4]. …”

Section: Evaluating Methods For Edge Embeddednessmentioning

confidence: 99%

Untangling Hairballs

Nocaj

Ortmann

Brandes

2014

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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Abstract. Small-world graphs have characteristically low average distance and thus cause force-directed methods to generate drawings that look like hairballs. This is by design as the inherent objective of these methods is a globally uniform edge length or, more generally, accurate distance representation. The problem arises in graphs of high density or high conductance, and in the presence of high-degree vertices, all of which tend to pull vertices together and thus clutter variation in local density.We here propose a method to draw online social networks, a special class of hairball graphs. The method is based on a spanning subgraph that is sparse but connected and consists of strong ties holding together communities. To identify these ties we propose a novel measure of embeddedness. It is based on a weighted accumulation of triangles in quadrangles and can be determined efficiently. An evaluation on empirical and generated networks indicates that our approach improves upon previous methods using other edge indices. Although primarily designed to achieve more informative drawings, our spanning subgraph may also serve as a sparsifier that trims a hairball graph before the application of a clustering algorithm.

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Section: Evaluating Methods For Edge Embeddednessmentioning

confidence: 99%

Untangling Hairballs

Nocaj

Ortmann

Brandes

2014

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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“…6. Embedding quality We measure this using the P-stress function [8], a variant of stress [9] that does not penalise unconnected nodes being more than their desired distance apart. It measures the separation between each pair of nodes u, v ∈ V in the drawing and their ideal distance d uv proportional to the graph theoretic path between them: where M (θ) is an "M-shaped function" over [0, π/2] that highly penalizes edges which are almost but not quite axis-aligned and gives a lower penalty for edges midway between horizontal and vertical.…”

Section: Aesthetic Criteriamentioning

confidence: 99%

Incremental Grid-Like Layout Using Soft and Hard Constraints

et al. 2013

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Abstract. We explore various techniques to incorporate grid-like layout conventions into a force-directed, constraint-based graph layout framework. In doing so we are able to provide high-quality layout-with predominantly axis-aligned edges-that is more flexible than previous grid-like layout methods and which can capture layout conventions in notations such as SBGN (Systems Biology Graphical Notation). Furthermore, the layout is easily able to respect user-defined constraints and adapt to interaction in online systems and diagram editors such as Dunnart.

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“…De Leeuw's accurate SMACOF [5] monotonically converges to a stationary point by minimizing a quadratic approximation at each iteration, resulting in provably linear convergence but at a large cost of O(N 2 L) per iteration. Gansner et al [10] use a SMACOFbased approach to stress majorization for graphs, but the sparsification and edge-weighting modifications they propose are not suitable for general MDS because in general, data topology is unknown. Computing the nearest-neighbor topology of general datasets is an O(N 2 ) pre-processing procedure.…”

Section: B Distance Scaling By Nonlinear Optimizationmentioning

confidence: 99%

Glimmer: Multilevel MDS on the GPU

Ingram

Munzner

Olano

2009

IEEE Trans. Visual. Comput. Graphics

162

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Abstract-We present Glimmer, a new multilevel algorithm for multidimensional scaling designed to exploit modern graphics processing unit (GPU) hardware. We also present GPU-SF, a parallel, force-based subsystem used by Glimmer. Glimmer organizes input into a hierarchy of levels and recursively applies GPU-SF to combine and refine the levels. The multilevel nature of the algorithm makes local minima less likely while the GPU parallelism improves speed of computation. We propose a robust termination condition for GPU-SF based on a filtered approximation of the normalized stress function. We demonstrate the benefits of Glimmer in terms of speed, normalized stress, and visual quality against several previous algorithms for a range of synthetic and real benchmark datasets. We also show that the performance of Glimmer on GPUs is substantially faster than a CPU implementation of the same algorithm.

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Graph Drawing by Stress Majorization

Cited by 303 publications

References 16 publications

Untangling Hairballs

Untangling Hairballs

Incremental Grid-Like Layout Using Soft and Hard Constraints

Glimmer: Multilevel MDS on the GPU

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