An algorithm for drawing general undirected graphs
Information Processing Letters
Updating the inverse of a matrix
SIAM Review
Graph drawing by force-directed placement
Software—Practice & Experience
A linear iteration time layout algorithm for visualising high-dimensional data
Proceedings of the 7th conference on Visualization '96
Drawing graphs to convey proximity: an incremental arrangement method
ACM Transactions on Computer-Human Interaction (TOCHI)
FADE: Graph Drawing, Clustering, and Visual Abstraction
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Graph Drawing by High-Dimensional Embedding
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
ACE: A Fast Multiscale Eigenvectors Computation for Drawing Huge Graphs
INFOVIS '02 Proceedings of the IEEE Symposium on Information Visualization (InfoVis'02)
Clustering Large Graphs via the Singular Value Decomposition
Machine Learning
Fast monte-carlo algorithms for finding low-rank approximations
Journal of the ACM (JACM)
Glimmer: Multilevel MDS on the GPU
IEEE Transactions on Visualization and Computer Graphics
Eigensolver methods for progressive multidimensional scaling of large data
GD'06 Proceedings of the 14th international conference on Graph drawing
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Graph drawing by stress majorization
GD'04 Proceedings of the 12th international conference on Graph Drawing
Drawing large graphs with a potential-field-based multilevel algorithm
GD'04 Proceedings of the 12th international conference on Graph Drawing
The laplacian paradigm: emerging algorithms for massive graphs
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Two-Way Multidimensional Scaling: A Review
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Graph drawing by subspace optimization
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
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Optimizing a stress model is a natural technique for drawing graphs: one seeks an embedding into Rd which best preserves the induced graph metric. Current approaches to solving the stress model for a graph with |𝒱| nodes and |ɛ| edges require the full all-pairs shortest paths (APSP) matrix, which takes O(|𝒱|2 log |ɛ|+|𝒱‖ɛ|) time and O(|𝒱|2) space. We propose a novel algorithm based on a low-rank approximation to the required matrices. The crux of our technique is an observation that it is possible to approximate the full APSP matrix, even when only a small subset of its entries are known. Our algorithm takes time O(k|𝒱|+|𝒱|log|𝒱|+|ɛ|) per iteration with a preprocessing time of O(k3+ k(|ɛ|+|𝒱| log |𝒱|) + k2|𝒱|) and memory usage of O(k|𝒱|), where a user-defined parameter k trades off quality of approximation with running time and space. We give experimental results which show, to the best of our knowledge, the largest (albeit approximate) full stress model based layouts to date. © 2012 Wiley Periodicals, Inc.