Strict confluent drawing

We define strict confluent drawing, a form of confluent drawing in which the existence of an edge is indicated by the presence of a smooth path through a system of arcs and junctions (without crossings), and in which such a path, if it exists, must be unique. We prove that it is NP-complete to determine whether a given graph has a strict confluent drawing but polynomial to determine whether it has an outerplanar strict confluent drawing with a fixed vertex ordering (a drawing within a disk, with the vertices placed in a given order on the boundary).

[1]  David Eppstein,et al.  Delta-Confluent Drawings , 2005, Graph Drawing.

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

[3]  Hong Zhou,et al.  Geometry-Based Edge Clustering for Graph Visualization , 2008, IEEE Transactions on Visualization and Computer Graphics.

[4]  Kenneth Stephenson,et al.  A circle packing algorithm , 2003, Comput. Geom..

[5]  Michael J. Pelsmajer,et al.  Train Tracks and Confluent Drawings , 2006, Algorithmica.

[6]  David Eppstein,et al.  Confluent Hasse Diagrams , 2013, J. Graph Algorithms Appl..

[7]  Martin Nöllenburg,et al.  Drawing Graphs and Maps with Curves , 2013 .

[8]  Kim Marriott,et al.  Integrating Edge Routing into Force-Directed Layout , 2006, GD.

[9]  W. Marsden.  I and J , 2012 .

[10]  Bettina Speckmann,et al.  Strict Confluent Drawing , 2013 .

[11]  Helen C. Purchase,et al.  Which Aesthetic has the Greatest Effect on Human Understanding? , 1997, GD.

[12]  Christophe Hurter,et al.  Graph Bundling by Kernel Density Estimation , 2012, Comput. Graph. Forum.

[13]  David Eppstein,et al.  Confluent Layered Drawings , 2006, Algorithmica.

[14]  David Lichtenstein,et al.  Planar Formulae and Their Uses , 1982, SIAM J. Comput..

[15]  Jarke J. van Wijk,et al.  Force‐Directed Edge Bundling for Graph Visualization , 2009, Comput. Graph. Forum.

[16]  Danny Holten,et al.  Hierarchical Edge Bundles: Visualization of Adjacency Relations in Hierarchical Data , 2006, IEEE Transactions on Visualization and Computer Graphics.

[17]  Bojan Mohar,et al.  A polynomial time circle packing algorithm , 1993, Discret. Math..

[18]  Michael A. Bekos,et al.  Smooth Orthogonal Layouts , 2012, Graph Drawing.

[19]  Massimo Ancona,et al.  Confluent Drawing Algorithms Using Rectangular Dualization , 2010, GD.

[20]  David Eppstein,et al.  Journal of Graph Algorithms and Applications Confluent Drawings: Visualizing Non-planar Diagrams in a Planar Way , 2022 .

[21]  Michael Hirsch,et al.  Biclique Edge Cover Graphs and Confluent Drawings , 2006, Graph Drawing.

[22]  Kurt Mehlhorn,et al.  From Algorithms to Working Programs: On the Use of Program Checking in LEDA , 1998, MFCS.

[23]  Seth M. Malitz,et al.  On the angular resolution of planar graphs , 1992, STOC '92.