In the constrained planarity setting, we ask whether a graph admits a planar
drawing that additionally satisfies a given set of constraints. These
constraints are often derived from very natural problems; prominent examples
are Level Planarity, where vertices have to lie on given horizontal lines
indicating a hierarchy, and Clustered Planarity, where we additionally draw the
boundaries of clusters which recursively group the vertices in a crossing-free
manner. Despite receiving significant amount of attention and substantial
theoretical progress on these problems, only very few of the found solutions
have been put into practice and evaluated experimentally.
In this paper, we describe our implementation of the recent quadratic-time
algorithm by Bl\"asius et al. [TALG Vol 19, No 4] for solving the problem
Synchronized Planarity, which can be seen as a common generalization of several
constrained planarity problems, including the aforementioned ones. Our
experimental evaluation on an existing benchmark set shows that even our
baseline implementation outperforms all competitors by at least an order of
magnitude. We systematically investigate the degrees of freedom in the
implementation of the Synchronized Planarity algorithm for larger instances and
propose several modifications that further improve the performance. Altogether,
this allows us to solve instances with up to 100 vertices in milliseconds and
instances with up to 100 000 vertices within a few minutes.Comment: to appear in Proceedings of ALENEX 202