Graph layering by promotion of nodes

This work contributes to the wide research area of visualization of hierarchical graphs. We present a new polynomial-time heuristic which can be integrated into the Sugiyama method for drawing hierarchical graphs. Our heuristic, which we call Promote Layering (PL), is applied to the output of the layering phase of the Sugiyama method. PL is a simple and easy to implement algorithm which decreases the number of so-called dummy (or virtual) nodes in a layered directed acyclic graph. In particular, we propose applying PL after the longest-path layering algorithm and we present an extensive empirical evaluation of this layering technique.

[1]  John N. Warfield,et al.  Crossing Theory and Hierarchy Mapping , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  Arne Frick Upper Bounds on the Number of Hidden Nodes in Sugiyama's Algorithm , 1996, Graph Drawing.

[3]  Kurt Mehlhorn,et al.  The LEDA Platform of Combinatorial and Geometric Computing , 1997, ICALP.

[4]  Y.-K. Kwok,et al.  Static scheduling algorithms for allocating directed task graphs to multiprocessors , 1999, CSUR.

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

[6]  Jürgen Branke,et al.  Width-restricted layering of acyclic digraphs with consideration of dummy nodes , 2002, Inf. Process. Lett..

[7]  Nikola S. Nikolov,et al.  How to Layer a Directed Acyclic Graph , 2001, GD.

[8]  Emden R. Gansner,et al.  A Technique for Drawing Directed Graphs , 1993, IEEE Trans. Software Eng..

[9]  Xuemin Lin,et al.  How to draw a directed graph , 1989, [Proceedings] 1989 IEEE Workshop on Visual Languages.

[10]  Ronald L. Graham,et al.  Optimal scheduling for two-processor systems , 1972, Acta Informatica.

[11]  T. C. Hu Parallel Sequencing and Assembly Line Problems , 1961 .

[12]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[13]  Nikola S. Nikolov,et al.  A Branch-and-Cut Approach to the Directed Acyclic Graph Layering Problem , 2002, Graph Drawing.

[14]  Jeffrey D. Ullman,et al.  NP-Complete Scheduling Problems , 1975, J. Comput. Syst. Sci..

[15]  Kozo Sugiyama,et al.  Graph Drawing by the Magnetic Spring Model , 1995, J. Vis. Lang. Comput..

[16]  Giuseppe Liotta,et al.  An Experimental Comparison of Four Graph Drawing Algorithms , 1997, Comput. Geom..

[17]  Marie-Jose Carpano,et al.  Automatic Display of Hierarchized Graphs for Computer-Aided Decision Analysis , 1980, IEEE Transactions on Systems, Man, and Cybernetics.