Slanted Orthogonal Drawings

We introduce a new model that we call slanted orthogonal graph drawing. While in traditional orthogonal drawings each edge is made of axis-aligned line-segments, in slanted orthogonal drawings intermediate diagonal segments on the edges are also permitted, which allows for: ai??smoothening the bends of the produced drawing as they are replaced by pairs of "half-bends", and, bi??emphasizing the crossings of the drawing as they always appear at the intersection of two diagonal segments. We present an approach to compute bend-optimal slanted orthogonal representations, an efficient heuristic to compute close-to-optimal drawings in terms of the total number of bends using quadratic area, and a corresponding LP formulation, when insisting on bend optimality. On the negative side, we show that bend-optimal slanted orthogonal drawings may require exponential area.

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

[2]  Charles E. Leiserson,et al.  Area-efficient graph layouts , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[3]  Ioannis G. Tollis,et al.  Planar grid embedding in linear time , 1989 .

[4]  Andreas Karrenbauer,et al.  Accelerated Bend Minimization , 2012, J. Graph Algorithms Appl..

[5]  Jan van Leeuwen,et al.  Algorithms — ESA '94 , 1994, Lecture Notes in Computer Science.

[6]  Charles E. Leiserson,et al.  Area-Efficient Graph Layouts (for VLSI) , 1980, FOCS.

[7]  Goos Kant,et al.  A better heuristic for orthogonal graph drawings , 1998, Comput. Geom..

[8]  Leslie G. Valiant,et al.  Universality considerations in VLSI circuits , 1981, IEEE Transactions on Computers.

[9]  Roberto Tamassia,et al.  On Embedding a Graph in the Grid with the Minimum Number of Bends , 1987, SIAM J. Comput..

[10]  Michael Kaufmann,et al.  On Improving Orthogonal Drawings: The 4M-Algorithm , 1998, GD.

[11]  Michael Kaufmann,et al.  Drawing High Degree Graphs with Low Bend Numbers , 1995, GD.

[12]  Alexander Wolff,et al.  Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming , 2011, IEEE Transactions on Visualization and Computer Graphics.