GD 1998: Graph Drawing pp 462-463

# Adding Constraints to an Algorithm for Orthogonal Graph Drawing

• Roland Wiese
• Michael Kaufmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1547)

## Abstract

There are two kinds of approaches for orthogonal graph drawing: one supports planar and almost planar graphs (Giotto [6], Kandinsky) and is based on a mincost flow algorithm. The second does not take planarity into account. It is therefore conceptually much simpler and runs in linear-time. Representatives of such concepts are the papers [5,3,2]. In a variant of this last paper, Biedl/Kaufmann [4] achieve the theoretically best area bound. The idea is the following: The graph is drawn such that each edge bends exactly once. Outgoing edges leave the vertex from the right or left side, incoming edges arrive at the top or bottom side. Edges are directed in a quasi-s-t-ordering such that each vertex gets at least one incoming and one outgoing edge. Then we assign disjoint rows to the vertices such that the number of outgoing edges leaving the vertex v to different directions is nearly balanced. The same is done for the column assignment where the numbers of incoming edges from different sides has to be balanced. Applying this simple scheme yields an area bound of (m + n)/2 × (m + n)/2 for the graph. Making graph algorithms aware of constraints is a very important task. We do it here for the Biedl/Kaufmann scheme.

## References

1. 1.
Biedl, T.C., Orthogonal Graph Drawing: The 3-Phases method, Ph.D.thesis, 1997.Google Scholar
2. 2.
Biedl, T.C., B. Madden, I.G. Tollis, The 3-Phase Method: A Unified Approach to Orthogonal Graph Drawing, Proceedings of GD’97, LNCS 1353, 391–403, 1997.Google Scholar
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Biedl, T.C., G. Kant, A better heuristic for orthogoanl graph drawings. Proceedings of ESA’94, LNCS 855, 24–35, 1994.Google Scholar
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Biedl, T.C., M. Kaufmann, Area-Efficient Static and Incremental Drawings of High-Degree Graphs. Proceedings of ESA’97, LNCS 1284, 37–52, 1997.Google Scholar
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Papakostas, A., I.G. Tollis, Orthogonal drawing of high degree graphs with samll area and few bends, Proceedings of WADS’97, LNCS, 1997.Google Scholar
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Tamassia, R. On Embedding a Graph in the Grid with the Minimum Number of Bends, SIAM Journal of Computing, vol. 16, no. 3, 421–444, 1987.

© Springer-Verlag Berlin Heidelberg 1998

## Authors and Affiliations

• Roland Wiese
• 1
• Michael Kaufmann
• 1
1. 1.Wilhelm-Schickard-InstitutUniversität TübingenTübingenGermany