Multi-dimensional Orthogonal Graph Drawing with Small Boxes

Extended Abstract
  • David R. Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1731)


In this paper we investigate the general position model for the drawing of arbitrary degree graphs in the D-dimensional (D ≥ 2) orthogonal grid. In this model no two vertices lie in the same grid hyperplane. We show that for D ≥ 3, given an arbitrary layout and initial edge routing a crossing-free orthogonal drawing can be determined. We distinguish two types of algorithms. Our layout-based algorithm, given an arbitrary fixed layout, determines a degree-restricted orthogonal drawing with each vertex having aspect ratio two. Using a balanced lay-out this algorithm establishes improved bounds on the size of vertices for 2-D and 3-D drawings. Our routing-based algorithm produces 2-degree- restricted 3-D orthogonal drawings. One advantage of our approach in 3-D is that edges are typically routed on each face of a vertex; hence the produced drawings are more truly three-dimensional than those produced by some existing algorithms.


Graph Drawing Edge Route Orthogonal Grid Orthogonal Graph Positive Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • David R. Wood
    • 1
  1. 1.School of Computer Science and Software EngineeringMonash UniversityAustralia

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