COAST: A Convex Optimization Approach to Stress-Based Embedding

  • Emden R. Gansner
  • Yifan Hu
  • Shankar Krishnan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)


Visualizing graphs using virtual physical models is probably the most heavily used technique for drawing graphs in practice. There are many algorithms that are efficient and produce high-quality layouts. If one requires that the layout also respect a given set of non-uniform edge lengths, however, force-based approaches become problematic while energy-based layouts become intractable. In this paper, we propose a reformulation of the stress function into a two-part convex objective function to which we can apply semi-definite programming (SDP). We avoid the high computational cost associated with SDP by a novel, compact re-parameterization of the objective function using the eigenvectors of the graph Laplacian. This sparse representation makes our approach scalable. We provide experimental results to show that this method scales well and produces reasonable layouts while dealing with the edge length constraints.


Edge Length Stress Model Large Graph Graph Distance Graph Drawing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Emden R. Gansner
    • 1
  • Yifan Hu
    • 1
  • Shankar Krishnan
    • 1
  1. 1.AT&T Labs - ResearchFlorham ParkUSA

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