Algorithms for computing a parameterized st-orientation
Theoretical Computer Science
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Interesting representations of graphs results from mapping vertices into horizontal segments and edges into vertical segments drawn between visible vertex-segments. (Two parallel segments of a given set are visible if they can be joined by a segment orthogonal to them, which does not intersect any other segment.) Such representations are called visibility representations. These representations find applications in VLSI layout, algorithm animation, visual languages and CASE tools. We consider three types of visibility representations: (i) Weakvisibility representation, if two vertices are adjacent then their corresponding segments must be visible. (ii) ε-visibility representation, where vertices can be represented by open, closed, or semiclosed horizontal segments in the plane such that two vertices are adjacent if and only if their associated segments are visible. (iii) Strong-visibility representation, where vertices are represented by closed horizontal segments such that two vertices are adjacent if and only if their corresponding segments are visible. We discuss various types of visibility representations of planar graphs on the plane, cylinder, and sphere.