Rolling Upward Planarity Testing of Strongly Connected Graphs

A graph is upward planar if it can be drawn without edge crossings such that all edges point upward. Upward planar graphs have been studied on the plane, the standing and rolling cylinders. For all these surfaces, the respective decision problem \(\mathcal{NP}\)-hard in general. Efficient testing algorithms exist if the graph contains a single source and a single sink but only for the plane and standing cylinder.

[1]  Franz-Josef Brandenburg.  On the Curve Complexity of Upward Planar Drawings , 2012, CATS.

[2]  Petra Mutzel,et al.  A Linear Time Implementation of SPQR-Trees , 2000, GD.

[3]  Frank Harary,et al.  The number of caterpillars , 1973, Discret. Math..

[4]  Roberto Tamassia,et al.  Algorithms for Plane Representations of Acyclic Digraphs , 1988, Theor. Comput. Sci..

[5]  Gregory Gutin,et al.  Digraphs - theory, algorithms and applications , 2002 .

[6]  S. Mehdi Hashemi.  Digraph embedding , 2001, Discret. Math..

[7]  David Kelly.  Fundamentals of planar ordered sets , 1987, Discret. Math..

[8]  Christian Bachmaier,et al.  Classification of Planar Upward Embedding , 2011, Graph Drawing.

[9]  Roberto Tamassia,et al.  On the Computational Complexity of Upward and Rectilinear Planarity Testing , 1994, SIAM J. Comput..

[10]  Christian Bachmaier,et al.  The Duals of Upward Planar Graphs on Cylinders , 2012, WG.

[11]  Roberto Tamassia,et al.  On-Line Planarity Testing , 1989, SIAM J. Comput..

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

[13]  Christian Bachmaier,et al.  Drawing Recurrent Hierarchies , 2012, J. Graph Algorithms Appl..

[14]  Carsten Thomassen,et al.  Graphs on Surfaces , 2001, Johns Hopkins series in the mathematical sciences.

[15]  C. Thomassen.  Planar acyclic oriented graphs , 1989 .

[16]  Andrzej Kisielewicz,et al.  The Complexity of Upward Drawings on Spheres , 1997 .

[17]  Ardeshir Dolati,et al.  On the sphericity testing of single source digraphs , 2008, Discret. Math..

[18]  Meena Mahajan,et al.  Upper Bounds for Monotone Planar Circuit Value and Variants , 2009, computational complexity.

[19]  Kristoffer Arnsfelt Hansen.  Constant Width Planar Computation Characterizes ACC0 , 2005, Theory of Computing Systems.

[20]  Franz-Josef Brandenburg,et al.  Upward planar drawings on the standing and the rolling cylinders , 2014, Comput. Geom..

[21]  Jorge Urrutia,et al.  Light sources, obstructions and spherical orders , 1992, Discret. Math..

[22]  Carlo Mannino,et al.  Optimal Upward Planarity Testing of Single-Source Digraphs , 1993, ESA.

[23]  Meena Mahajan,et al.  Evaluating Monotone Circuits on Cylinders, Planes and Tori , 2006, STACS.