How to Draw Outerplanar Minimum Weight Triangulations
William Lenhart,Giuseppe Liotta +1 more
- pp 373-384
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This paper provides a complete characterization of minimum weight triangulations of regular polygons by studying the combinatorial properties of their dual trees and exploits this characterization to devise a linear time algorithm that receives as input a maximal outerplanar graph G and produces as output a straight-line drawing of G.Abstract:
In this paper we consider the problem of characterizing those graphs that can be drawn as minimum weight triangulations and answer the question for maximal outerplanar graphs. We provide a complete characterization of minimum weight triangulations of regular polygons by studying the combinatorial properties of their dual trees. We exploit this characterization to devise a linear time (real RAM) algorithm that receives as input a maximal outerplanar graph G and produces as output a straight-line drawing of G that is a minimum weight triangulation of the set of points representing the vertices of G.read more
Citations
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Book ChapterDOI
Drawable and Forbidden Minimum Weight Triangulations
William Lenhart,Giuseppe Liotta +1 more
TL;DR: This paper presents non-trivial classes of triangulations that are minimum weight drawable, along with corresponding linear time algorithms that take as input any graph from one of these classes and produce as output such a drawing.
Proceedings Article
A Near-Optimal Heuristic for Minimum Weight Triangulation of Convex Polygons (Extended Abstract).
TL;DR: In this article, a linear-time heuristic for minimum weight triangulation of convex polygons is presented, which achieves an approximation of length within a factor 1 + ϵ from the optimum.
Book ChapterDOI
Minimum Weight Drawings of Maximal Triangulations (Extended Abstract)
William Lenhart,Giuseppe Liotta +1 more
TL;DR: It is shown that all maximal triangulations whose skeleton is acyclic are minimum weight drawable, a recursive method for constructing infinitely many minimum weight Drawable Triangulations is presented, and it is proved that allmaximal triangulation whosekeleton is a maximal outerplanar graph are minimum Weight drawable.
References
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TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
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TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
Computational geometry. an introduction
TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Journal ArticleDOI
Graph theory with applications (revised edition), by J. A. Bondy and U.S.R. Murty. Pp x, 264. £5·95 paperback. 1977. SBN 0 333 22694 1 (Macmillan)
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Computational Geometry: An Introduction
TL;DR: In this article, the authors present a coherent treatment of computational geometry in the plane, at the graduate textbook level, and point out the way to the solution of the more challenging problems in dimensions higher than two.