A LinearTime Algorithm for BendOptimal Orthogonal Drawings of Biconnected Cubic Plane Graphs (Extended Abstract)Nakano, ShinIchi and Yoshikawa, Makiko (2001) A LinearTime Algorithm for BendOptimal Orthogonal Drawings of Biconnected Cubic Plane Graphs (Extended Abstract). In: Graph Drawing 8th International Symposium, GD 2000, September 20–23, 2000 , pp. 296307(Official URL: http://dx.doi.org/10.1007/3540445412_28). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540445412_28
AbstractAn orthogonal drawing of a plane graph G is a drawing of G with the given planar embedding in which each vertex is mapped to a point, each edge is drawn as a sequence of alternate horizontal and vertical line segments, and any two edges do not cross except at their common end. Observe that only a planar graph with the maximum degree four or less has an orthogonal drawing. The best known algorithm to find an orthogonal drawing runs in time $O(n^{7/4}\sqrt {\log n})$ for any plane graph with n vertices. In this paper we give a lineartime algorithm to find an orthogonal drawing of a given biconnected cubic plane graph with the minimum number of bends.
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