# The Bundled Crossing Number

• Md. Jawaherul Alam
• Martin Fink
• Sergey Pupyrev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

## Abstract

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 $$\frac{6c}{c-2}$$-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 $$\frac{6c}{c-3}$$ for graphs with at least cn edges for $$c > 3$$.

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© Springer International Publishing AG 2016

## Authors and Affiliations

• Md. Jawaherul Alam
• 1
• Martin Fink
• 2
• Sergey Pupyrev
• 3
• 4
Email author
1. 1.Department of Computer ScienceUniversity of CaliforniaIrvineUSA
2. 2.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
3. 3.Department of Computer ScienceUniversity of ArizonaTucsonUSA
4. 4.Institute of Mathematics and Computer ScienceUral Federal UniversityYekaterinburgRussia