Bipartite graphs, upward drawings, and planarity
Information Processing Letters
Upward planar drawing of single source acyclic digraphs
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
Journal of the ACM (JACM)
On the Computational Complexity of Upward and Rectilinear Planarity Testing
SIAM Journal on Computing
An Approach for Mixed Upward Planarization
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Upward Planarity Testing of Outerplanar Dags
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Layer-free upward crossing minimization
Journal of Experimental Algorithmics (JEA)
Upward Spirality and Upward Planarity Testing
SIAM Journal on Discrete Mathematics
Fixed-Parameter tractable algorithms for testing upward planarity
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Upward planarity testing of embedded mixed graphs
GD'11 Proceedings of the 19th international conference on Graph Drawing
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A directed acyclic graph is upward planar if it allows a drawing without edge crossings where all edges are drawn as curves with monotonously increasing y-coordinates. The problem to decide whether a graph is upward planar or not is NP-complete in general, and while special graph classes are polynomial time solvable, there is not much known about solving the problem for general graphs in practice. The only attempt so far was a branch-and-bound algorithm over the graph's triconnectivity structure which was able to solve sparse graphs. In this paper, we propose a fundamentally different approach, based on the seemingly novel concept of ordered embeddings. We carefully model the problem as a special SAT instance, i.e., a logic formula for which we check satisfiability. Solving these SAT instances allows us to decide upward planarity for arbitrary graphs. We then show experimentally that this approach seems to dominate the known alternative approaches and is able to solve traditionally used graph drawing benchmarks effectively.