Open Rectangle-of-Influence Drawings of Non-triangulated Planar Graphs
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.
KeywordsProximity drawings Rectangle-of-Influence drawings Angular labeling
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