# Multi-dimensional Orthogonal Graph Drawing with Small Boxes

## Abstract

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.

## Keywords

Graph Drawing Edge Route Orthogonal Grid Orthogonal Graph Positive Vertex## References

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