Drawable and forbidden minimum weight triangulations

Extended abstract
  • William Lenhart
  • Giuseppe Liotta
Planarity and Crossings
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)

Abstract

A graph is minimum weight drawable if it admits a straight-line drawing that is a minimum weight triangulation of the set of points representing the vertices of the graph. In this paper we consider the problem of characterizing those graphs that are minimum weight drawable. Our contribution is twofold: We show that there exist infinitely many triangulations that are not minimum weight drawable. Furthermore, we present non-trivial classes of triangulations that are minimum weight drawable, along with corresponding linear time (real RAM) algorithms that take as input any graph from one of these classes and produce as output such a drawing. One consequence of our work is the construction of triangulations that are minimum weight drawable but none of which is Delaunay drawable—that is, drawable as a Delaunay triangulation.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • William Lenhart
    • 1
  • Giuseppe Liotta
    • 2
  1. 1.Department of Computer ScienceWilliams CollegeWilliamstown
  2. 2.Dipartimento di Informatics e SistemisticaUniversità di Roma ‘La Sapienza’RomaItalia

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