Stress Majorization with Orthogonal Ordering Constraints

The adoption of the stress-majorization method from multi-dimensio- nal scaling into graph layout has provided an improved mathematical basis and better convergence properties for so-called “force-directed placement” techniques. In this paper we give an algorithm for augmenting such stress-majorization techniques with orthogonal ordering constraints and we demonstrate several graph-drawing applications where this class of constraints can be very useful.

[1]  Y. Koren,et al.  Dig-CoLa: directed graph layout through constrained energy minimization , 2005, IEEE Symposium on Information Visualization, 2005. INFOVIS 2005..

[2]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[3]  Satoru Kawai,et al.  An Algorithm for Drawing General Undirected Graphs , 1989, Inf. Process. Lett..

[4]  Richard F. Barrett,et al.  Matrix Market: a web resource for test matrix collections , 1996, Quality of Numerical Software.

[5]  Seok-Hee Hong,et al.  The Metro Map Layout Problem , 2004, InVis.au.

[6]  Kozo Sugiyama,et al.  Layout Adjustment and the Mental Map , 1995, J. Vis. Lang. Comput..

[7]  Joe Marks,et al.  An interactive constraint-based system for drawing graphs , 1997, UIST '97.

[8]  J. Shewchuk An Introduction to the Conjugate Gradient Method Without the Agonizing Pain , 1994 .

[9]  Kim Marriott,et al.  Constrained Graph Layout , 1996, Constraints.

[10]  J. Kalbfleisch Statistical Inference Under Order Restrictions , 1975 .

[11]  David Harel,et al.  Combining Hierarchy and Energy for Drawing Directed Graphs , 2003 .

[12]  Yehuda Koren,et al.  Graph Drawing by Stress Majorization , 2004, GD.

[13]  Mitsuhiko Toda,et al.  Methods for Visual Understanding of Hierarchical System Structures , 1981, IEEE Transactions on Systems, Man, and Cybernetics.