Bounded Degree Book Embeddings and Three-Dimensional Orthogonal Graph Drawing

  • David R. Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2265)


A book embedding of a graph consists of a linear ordering of the vertices along a line in 3-space (the spine), and an assignment of edges to half-planes with the spine as boundary (the pages), so that edges assigned to the same page can be drawn on that page without crossings. Given a graph G = (V,E), let f : V → ℕ be a function such that 1 ≤ f(υ) ≤ deg(υ). We present a Las Vegas algorithm which produces a book embedding of G with \( O(\sqrt {|E| \cdot \max _\upsilon \left\lceil {\deg (\upsilon )/f(\upsilon )} \right\rceil } ) \) pages, such that at most f(v) edges incident to a vertex v are on a single page. This algorithm generalises existing results for book embeddings. We apply this algorithm to produce 3-D orthogonal drawings with one bend per edge and O(∣V3/2E∣) volume, and single-row drawings with two bends per edge and the same volume. In the produced drawings each edge is entirely contained in some Z-plane; such drawings are without so-called cross-cuts, and are particularly appropriate for applications in multilayer VLSI. Using a different approach, we achieve two bends per edge with O(∣V ∣∣E∣) volume but with cross-cuts. These results establish improved bounds for the volume of 3-D orthogonal graph drawings.


Bipartite Graph Edge Incident Edge Route Single Page Canonical Ordering 
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 2002

Authors and Affiliations

  • David R. Wood
    • 1
  1. 1.Basser Department of Computer ScienceThe University of SydneySydneyAustralia

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