On Planar Polyline DrawingsZhang, Huaming and Sadasivam, Sadish (2008) On Planar Polyline Drawings. In: Graph Drawing 15th International Symposium, GD 2007, September 2426, 2007 , pp. 213218(Official URL: http://dx.doi.org/10.1007/9783540775379_22). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783540775379_22
AbstractWe present a linear time algorithm that produces a planar polyline drawing for a plane graph with $n$ vertices in a grid of size bounded by $(p+1) times (n2)$, where $p leq (lfloor frac2n53rfloor)$. It uses at most $p leq lfloorfrac2n53rfloor$ bends, and each edge uses at most one bend. Compared with the area optimal polyline drawing algorithm in [3], our algorithm uses a larger grid size bound in trade for a smaller bound on the total number of bends. Their bend bound is $(n2)$. Our algorithm is based on a transformation from Schnyder's realizers [6, 7] of maximal plane graphs to transversal structures [4, 5] for maximal internally 4connected plane graphs. This transformation reveals important relations between the two combinatorial structures for plane graphs, which is of independent interest.
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