Before revision:  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 .
After revision:  These results make use of the connection between bundled crossings and graph genus .