Unit Bar-Visibility Layouts of Triangulated Polygons

  • Alice M. Dean
  • Ellen Gethner
  • Joan P. Hutchinson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3383)

Abstract

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Alice M. Dean
    • 1
  • Ellen Gethner
    • 2
  • Joan P. Hutchinson
    • 3
  1. 1.Skidmore CollegeSaratoga SpringsUSA
  2. 2.University of Colorado at DenverDenverUSA
  3. 3.Macalester CollegeSt. PaulUSA

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