Bundled Crossings Revisited
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An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges into bundles when they travel in parallel. 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 minimize the number of bundled crossings. We consider two settings. In the first setting, a graph is given and the goal is to find a bundled drawing with at most k crossings. We show that the problem is NP-hard when we require a simple drawing. Our main result is an FPT algorithm (in k) when we require a simple circular layout. These results make use of the connection between bundled crossings and graph genus. In the second setting, we bundle a given drawing to minimize the number of bundled crossings. We investigate storyline visualizations (for which the bundled drawing problem has been well studied). We show that testing if a given visualization with m characters can be bundled into k crossings is FPT in m with singly-exponential runtime.
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