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In the constrained planarity setting, we ask whether a graph admits a planardrawing that additionally satisfies a given set of constraints. Theseconstraints are often derived from very natural problems; prominent examplesare Level Planarity, where vertices have to lie on given horizontal linesindicating a hierarchy, and Clustered Planarity, where we additionally draw theboundaries of clusters which recursively group the vertices in a crossing-freemanner. Despite receiving significant amount of attention and substantialtheoretical progress on these problems, only very few of the found solutionshave been put into practice and evaluated experimentally.  In this paper, we describe our implementation of the recent quadratic-timealgorithm by Bl\"asius et al. [TALG Vol 19, No 4] for solving the problemSynchronized Planarity, which can be seen as a common generalization of severalconstrained planarity problems, including the aforementioned ones. Ourexperimental evaluation on an existing benchmark set shows that even ourbaseline implementation outperforms all competitors by at least an order ofmagnitude. We systematically investigate the degrees of freedom in theimplementation of the Synchronized Planarity algorithm for larger instances andpropose several modifications that further improve the performance. Altogether,this allows us to solve instances with up to 100 vertices in milliseconds andinstances with up to 100 000 vertices within a few minutes.

Constrained Planarity in Practice -- Engineering the Synchronized Planarity Algorithm