On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Rectangular grid drawings of plane graphs
Computational Geometry: Theory and Applications
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Rectangular Drawings of Plane Graphs Without Designated Corners
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
A New Minimum Cost Flow Algorithm with Applications to Graph Drawing
GD '96 Proceedings of the Symposium on Graph Drawing
Two Algorithms for Finding Rectangular Duals of Planar Graphs
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
On the Compuational Complexity of Upward and Rectilinear Planarity Testing
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Bend-Minimum Orthogonal Drawings of Plane 3-Graphs
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
The DFS-heuristic for orthogonal graph drawing
Computational Geometry: Theory and Applications
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An 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(n7/4√log n) for any plane graph with n vertices. In this paper we give a linear-time algorithm to find an orthogonal drawing of a given biconnected cubic plane graph with the minimum number of bends.