Fundamentals of planar ordered sets
Discrete Mathematics
Optimization
Bipolar orientations revisited
Discrete Applied Mathematics - Special issue: Fifth Franco-Japanese Days, Kyoto, October 1992
Optimal Upward Planarity Testing of Single-Source Digraphs
SIAM Journal on Computing
A new approximation algorithm for the planar augmentation problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Computing Orthogonal Drawings with the Minimum Number of Bends
IEEE Transactions on Computers
Weighted Visibility Graphs of Bars and Related Flow Problems (Extended Abstract)
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Upward Embeddings and Orientations of Undirected Planar Graphs
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
A New Minimum Cost Flow Algorithm with Applications to Graph Drawing
GD '96 Proceedings of the Symposium on Graph Drawing
On the Compuational Complexity of Upward and Rectilinear Planarity Testing
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Bar-representable visibility graphs and a related network flow problem
Bar-representable visibility graphs and a related network flow problem
Upward Embeddings and Orientations of Undirected Planar Graphs
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
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An upward embedding of an embedded planar graph states, for each vertex v, which edges are incident to v "above" or "below" and, in turn, induces an upward orientation of the edges. In this paper we characterize the set of all upward embeddings and orientations of a plane graph by using a simple flow model. We take advantage of such a flow model to compute upward orientations with the minimum number of sources and sinks of 1-connected graphs. Our theoretical results allow us to easily compute visibility representations of 1-connected graphs while having a certain control over the width and the height of the computed drawings, and to deal with partial assignments of the upward embeddings "underlying" the visibility representations.