Geodesic
Accelerated Bend Minimization
Journal of Graph Algorithms and Applications, Special Issue on Selected Papers from the Nineteenth International Symposium on Graph Drawing, GD 2011 , Tome 16 (2012) no. 3, pp. 635-650.

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We present an O( n3/2) algorithm for minimizing the number of bends in an orthogonal drawing of a plane graph. It has been posed as a long standing open problem at Graph Drawing 2003, whether the bound of O(n7/4√log n) shown by Garg and Tamassia in 1996 could be improved. To answer this question, we show how to solve the uncapacitated min-cost flow problem on a planar bidirected graph with bounded costs and face sizes in O( n3/2) time. 
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     author = {Sabine Cornelsen and Andreas Karrenbauer},
     title = {Accelerated {Bend} {Minimization}},
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Sabine Cornelsen; Andreas Karrenbauer. Accelerated Bend Minimization. Journal of Graph Algorithms and Applications, 
							Special Issue on Selected Papers from the Nineteenth International Symposium on Graph Drawing, GD 2011
					, Tome 16 (2012) no. 3, pp. 635-650. doi : 10.7155/jgaa.00265. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00265/

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