Geodesic
Box-Rectangular Drawings of Planar Graphs
Journal of Graph Algorithms and Applications, Special Issue on Selected Papers from the Seventh International Workshop on Algorithms and Computation, WALCOM 2013 , Tome 17 (2013) no. 6, pp. 629-646.

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A plane graph is a planar graph with a fixed planar embedding in the plane. In a box- rectangular drawing of a plane graph, every vertex is drawn as a rectangle, called a box, each edge is drawn as either a horizontal line segment or a vertical line segment, and the contour of each face is drawn as a rectangle. A planar graph is said to have a box-rectangular drawing if at least one of its plane embeddings has a box-rectangular drawing. Rahman et al. gave a necessary and sufficient condition for a plane graph to have a box-rectangular drawing and developed a linear-time algorithm to draw a box-rectangular drawing of a plane graph if it exists. Since a planar graph G may have an exponential number of planar embeddings, determining whether G has a box-rectangular drawing or not using the algorithm of Rahman et al. for each planar embedding of G takes exponential time. Thus to develop an efficient algorithm to examine whether a planar graph has a box-rectangular drawing or not is a non-trivial problem. In this paper we give a linear-time algorithm to determine whether a planar graph G has a box-rectangular drawing or not, and to find a box-rectangular drawing of G if it exists. 
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     author = {Md. Manzurul Hasan and Md. Saidur Rahman and Md. Rezaul Karim},
     title = {Box-Rectangular {Drawings} of {Planar} {Graphs}},
     journal = {Journal of Graph Algorithms and Applications},
     pages = {629--646},
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Md. Manzurul Hasan; Md. Saidur Rahman; Md. Rezaul Karim. Box-Rectangular Drawings of Planar Graphs. Journal of Graph Algorithms and Applications, 
							Special Issue on Selected Papers from the Seventh International Workshop on Algorithms and Computation, WALCOM 2013
					, Tome 17 (2013) no. 6, pp. 629-646. doi : 10.7155/jgaa.00309. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00309/

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