Upward Planarity Testing: A Computational Study

Abstract

A directed acyclic graph (DAG) is upward planar if it can be drawn without any crossings while all edges-when following them in their direction-are drawn with strictly monotonously increasing ycoordinates. Testing whether a graph allows such a drawing is known to be NP-complete, but there is a substantial collection of different algorithmic approaches known in literature. In this paper, we give an overview of the known algorithms, ranging from combinatorial FPT and branch-and-bound algorithms to ILP and SAT formulations. Most approaches of the first class have only been considered from the theoretical point of view, but have never been implemented. For the first time, we give an extensive experimental comparison between virtually all known approaches to the problem. Furthermore, we present a new SAT formulation based on a recent theoretical result by Fulek et al. [8], which turns out to perform best among all known algorithms.

Hanani-Tutte for Radial Planarity

“…The full Hanani-Tutte theorem for level-planarity was established only more recently [9], and it led to a quadratic time level-planarity test. A computational study of Chimani and Zeranski [4] of various algorithms for upward planarity testing (an NP-complete problem related to level-planarity), showed that the algorithm based on the Hanani-Tutte characterization of level-planarity performs very well in practice (it beats all other algorithms in nearly all scenarios).…”

Clustered Planarity Testing Revisited

“…We remark that there exist more efficient algorithms for planarity testing using the Hanani-Tutte theorem such as those in [14,15], which run in linear time; see also [36,Section 1.4.1]. Moreover, in the case of x-monotone drawings a computational study [5] showed that the Hanani-Tutte approach [18] performs really well in practice. This should come as no surprise, since Hanani-Tutte theory seems to provide solid theoretical foundations for graph planarity that bring together its combinatorial, algebraic, and computational aspects [37].…”

Clustered Planarity Testing Revisited

“…We remark that there exist more efficient algorithms for planarity testing using the Hanani-Tutte theorem such as those in [14,15], which run in linear time; see also [36,Section 1.4.1]. Moreover, in the case of x-monotone drawings a computational study [5] showed that the Hanani-Tutte approach [18] performs really well in practice. This should come as no surprise, since Hanani-Tutte theory seems to provide solid theoretical foun-dations for graph planarity that bring together its combinatorial, algebraic, and computational aspects [37].…”