Comparison of Maximal Upward Planar Subgraph Computation Algorithms

A digraph G = (V, E) is upward planar if it has a planar drawing with all edges pointing upward. A subgraph G̃ of a digraph G with an upward planar drawing is called a maximal upward planar subgraph of G if the addition of any edge in G\G to G̃ causes non-upward planarity. Binucci et al. showed that finding even the maximum upward planar subgraph of an embedded digraph Gφ is NP-Complete [1]. In this paper, we compare different algorithms to find maximal upward planar subgraph of an embedded digraph. We also use a large test suite of embedded digraphs to gain a deeper understanding of upward planarity and see how the different heuristics perform in practice.