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<p>A four-pass algorithm for drawing directed graphs is presented. The fist pass finds an optimal rank assignment using a network simplex algorithm. The seconds pass sets the vertex order within ranks by an iterative heuristic, incorporating a novel weight function and local transpositions to reduce crossings. The third pass finds optimal coordinates for nodes by constructing and ranking an auxiliary graph. The fourth pass makes splines to draw edges. The algorithm creates good drawings and is fast.</p>
directed graphs; four-pass algorithm; optimal rank assignment; network simplex algorithm; vertex order; iterative heuristic; novel weight function; local transpositions; optimal coordinates; auxiliary graph; splines; computer graphics; directed graphs; optimisation; splines (mathematics)
E.R. Gansner, S.C. North, K.-P. Vo, E. Koutsofios, "A Technique for Drawing Directed Graphs", IEEE Transactions on Software Engineering, vol. 19, no. , pp. 214-230, March 1993, doi:10.1109/32.221135
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