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Just Accepted
This paper has been accepted to be published in the JGAA Special issue on Selected papers from the Twenty-seventh International Symposium on Graph Drawing and Network Visualization, GD 2019. The paper will receive a volume, an issue number, and page numbers when the whole special issue will be published.
DOI: 10.7155/jgaa.00535
Bundled Crossings Revisited
Steven Chaplick,
Thomas C. van Dijk,
Myroslav Kryven,
Ji-won Park,
Alexander Ravsky, and
Alexander Wolff
Vol. 0, no. 0, pp. 0-0, 0. Regular paper.
Abstract An effective way to reduce clutter in
a graph drawing that has (many) crossings is to group
edges that travel in parallel into bundles.
Each edge can participate in many such bundles.
Any crossing in this bundled
graph occurs between two bundles, i.e., as a bundled crossing.
We consider the problem of bundled crossing minimization:
A graph is given and the goal is to find
a bundled drawing with at most $k$ bundled crossings.
We show that the problem is NP-hard when we require a simple drawing.
Our main result is an FPT algorithm (in $k$)
for simple circular layouts where vertices must be placed on
a circle and edges must be drawn inside the circle.
These results make use of the connection between bundled crossings
and graph genus. We also consider bundling crossings in a given
drawing, in particular for storyline visualizations.
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Submitted: November 2019.
Reviewed: January 2020.
Revised: April 2020.
Accepted: June 2020.
Final: June 2020.
Appeared on-line: June 2020.
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