Layout with Circular and Other Non-linear Constraints Using Procrustes Projection

  • Tim Dwyer
  • George Robertson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)


Recent work on constrained graph layout has involved projection of simple two-variable linear equality and inequality constraints in the context of majorization or gradient-projection based optimization. While useful classes of containment, alignment and rectangular non-overlap constraints could be built using this framework, a severe limitation was that the layout used an axis-separation approach such that all constraints had to be axis aligned. In this paper we use techniques from Procrustes Analysis to extend the gradient-projection approach to useful types of non-linear constraints. The constraints require subgraphs to be locally fixed into various geometries—such as circular cycles or local layout obtained by a combinatorial algorithm (e.g. orthogonal or layered-directed)—but then allow these sub-graph geometries to be integrated into a larger layout through translation, rotation and scaling.


Nonlinear Constraint Procrustes Analysis Layout Algorithm Separation Constraint Constraint Projection 
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-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tim Dwyer
    • 1
  • George Robertson
    • 1
  1. 1.Microsoft ResearchRedmondUSA

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