Edge crossings in drawings of bipartite graphs |
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Authors: | Peter Eades Nicholas C. Wormald |
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Affiliation: | (1) Department of Computer Science, University of Queensland, 4072 Queensland, Australia;(2) Department of Mathematics, University of Melbourne, 3052 Parkville, Victoria, Australia |
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Abstract: | Systems engineers have recently shown interest in algorithms for drawing directed graphs so that they are easy to understand and remember. Each of the commonly used methods has a step which aims to adjust the drawing to decrease the number of arc crossings. We show that the most popular strategy involves an NP-complete problem regarding the minimization of the number of arcs in crossings in a bipartite graph. The performance of the commonly employed barycenter heuristic for this problem is analyzed. An alternative method, the median heuristic, is proposed and analyzed. The new method is shown to compare favorably with the old in terms of performance guarantees. As a bonus, we show that the median heuristic performs well with regard to the total length of the arcs in the drawing. |
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Keywords: | Graph Bipartite graph Directed graph Edge crossing Median |
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