We study the algorithmic aspect of edge bundling. A bundled crossing in a drawing of a graph is a group of crossings between two sets of parallel edges. The bundled crossing number is the minimum number of bundled crossings that group all crossings in a drawing of the graph. We show that the bundled crossing number is closely related to the orientable genus of the graph. If multiple crossings and self-intersections of edges are allowed, the two values are identical; otherwise, the bundled crossing number can be higher than the genus. We then investigate the problem of minimizing the number of bundled crossings. For circular graph layouts with a fixed order of vertices, we present a constant-factor approximation algorithm. When the circular order is not prescribed, we get a 6c/c - 2 -approximation for a graph with n vertices having at least cn edges for c > 2. For general graph layouts, we develop an algorithm with an approximation factor of 6c/c - 3 for graphs with at least cn edges for c > 3.
CITATION STYLE
Alam, M. J., Fink, M., & Pupyrev, S. (2016). The bundled crossing number. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9801 LNCS, pp. 399–412). Springer Verlag. https://doi.org/10.1007/978-3-319-50106-2_31
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