Abstract
We present an \(\mathcal O( n^{3/2})\) 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 \(\mathcal O(n^{7/4}\sqrt{\log n})\) 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 \(\mathcal O(n^{3/2})\) time.
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Cornelsen, S., Karrenbauer, A. (2012). Accelerated Bend Minimization. In: van Kreveld, M., Speckmann, B. (eds) Graph Drawing. GD 2011. Lecture Notes in Computer Science, vol 7034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25878-7_12
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DOI: https://doi.org/10.1007/978-3-642-25878-7_12
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