Unit Bar-Visibility Layouts of Triangulated Polygons Extended Abstract
Dean, Alice M. and Gethner, Ellen and Hutchinson, Joan P. (2004) Unit Bar-Visibility Layouts of Triangulated Polygons Extended Abstract. In: Graph Drawing 12th International Symposium, GD 2004, September 29-October 2, 2004, New York, NY, USA , pp. 111-121 (Official URL: http://dx.doi.org/10.1007/978-3-540-31843-9_13).
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A triangulated polygon is a 2-connected maximal outerplanar graph. A unit bar-visibility graph (UBVG for short) is a graph whose vertices can be represented by disjoint, horizontal, unit-length bars in the plane so that two vertices are adjacent if and only if there is a non-degenerate, unobstructed, vertical band of visibility between the corresponding bars. We give combinatorial and geometric characterizations of the triangulated polygons that are UBVGs. To each triangulated polygon G we assign a character string with the property that G is a UBVG if and only if the string satisfies a certain regular expression. Given a string that satisfies this condition, we describe a linear-time algorithm that uses it to produce a UBV layout of G.
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