Computer aided layout of entity relationship diagrams
Journal of Systems and Software - Special double issue on the entity-relationship approach to databases and related software
Embedding rectilinear graphs in linear time
Information Processing Letters
On the Computational Complexity of Upward and Rectilinear Planarity Testing
SIAM Journal on Computing
Orthogonal Drawings of Plane Graphs without Bends
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Drawing graphs in the plane with high resolution
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Drawing Graphs with Right Angle Crossings
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
No-bend orthogonal drawings of series-parallel graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Exploring the relative importance of crossing number and crossing angle
Proceedings of the 3rd International Symposium on Visual Information Communication
Complexity of finding non-planar rectilinear drawings of graphs
GD'10 Proceedings of the 18th international conference on Graph drawing
Hardness of approximate compaction for nonplanar orthogonal graph drawings
GD'11 Proceedings of the 19th international conference on Graph Drawing
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A rectilinear drawing is an orthogonal grid drawing without bends, possibly with edge crossings, without any overlapping between edges, between vertices, or between edges and vertices. Rectilinear drawings without edge crossings (planar rectilinear drawings) have been extensively investigated in graph drawing. Testing rectilinear planarity of a graph is NP-complete [10]. Restricted cases of the planar rectilinear drawing problem, sometimes called the “no-bend orthogonal drawing problem”, have been well studied (see, for example,[13],[14],[15] ). In this paper, we study the problem of general non-planar rectilinear drawing; this problem has not received as much attention as the planar case. We consider a number of restricted classes of graphs and obtain a polynomial time algorithm, NP-hardness results, an FPT algorithm, and some bounds. We define a structure called a “4-cycle block”. We give a linear time algorithm to test whether a graph that consists of a single 4-cycle block has a rectilinear drawing, and draw it if such a drawing exists. We show that the problem is NP-hard for the graphs that consist of 4-cycle blocks connected by single edges, as well as the case where each vertex has degree 2 or 4. We present a linear time fixed-parameter tractable algorithm to test whether a degree-4 graph has a rectilinear drawing, where the parameter is the number of degree-3 and degree-4 vertices of the graph. We also present a lower bound on the area of rectilinear drawings, and a upper bound on the number of edges.