Adding Constraints to an Algorithm for Orthogonal Graph Drawing
There are two kinds of approaches for orthogonal graph drawing: one supports planar and almost planar graphs (Giotto , 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  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.
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