On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
On the Computational Complexity of Upward and Rectilinear Planarity Testing
SIAM Journal on Computing
Rectangle-of-influence drawings of four-connected plane graphs: extended abstract
APVis '05 proceedings of the 2005 Asia-Pacific symposium on Information visualisation - Volume 45
Handbook of Graph Drawing and Visualization (Discrete Mathematics and Its Applications)
Handbook of Graph Drawing and Visualization (Discrete Mathematics and Its Applications)
Closed rectangle-of-influence drawings for irreducible triangulations
Computational Geometry: Theory and Applications
Planar open rectangle-of-influence drawings with non-aligned frames
GD'11 Proceedings of the 19th international conference on Graph Drawing
GD'11 Proceedings of the 19th international conference on Graph Drawing
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A straight line drawing of a graph is an open weak rectangle-of-influence (RI) drawing if there is no vertex in the relative interior of the axis parallel rectangle induced by the end points of each edge. Despite recent interest of the graph drawing community in rectangle-of-influence drawings, no algorithm is known to test whether a graph has a planar open weak RI-drawing. In a recent paper, we showed how to test, for inner-triangulated planar graphs, whether they have a planar open weak RI-drawing with a non-aligned frame, i.e., the graph obtained from removing the interior of every filled triangle is drawn such that no two vertices have the same coordinate. In this paper, we generalize this to all planar graphs with a fixed planar embedding, even if some interior faces are not triangles. On the other hand, we show that if the planar embedding is not fixed, then deciding if a given planar graph has an open weak RI-drawing is NP-complete. NP-completeness holds even for open weak RI-drawings with non-aligned frames.