Computational geometry: an introduction
Computational geometry: an introduction
A new heuristic for minimum weight triangulation
SIAM Journal on Algebraic and Discrete Methods
Realizability of Delaunay triangulations
Information Processing Letters
Toughness and Delaunay triangulations
Discrete & Computational Geometry
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Computing the minimum weight triangulation of a set of linearly ordered points
Information Processing Letters
Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Computing a subgraph of the minimum weight triangulation
Computational Geometry: Theory and Applications
New algorithms and empirical findings on minimum weight triangulation heuristics (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Drawing outerplanar minimum weight triangulations
Information Processing Letters
Tight lower bounds for minimum weight triangulation heuristics
Information Processing Letters
Approaching the largest &bgr;-skeleton within a minimum weight triangulation
Proceedings of the twelfth annual symposium on Computational geometry
A (usually?) connected subgraph of the minimum weight triangulation
Proceedings of the twelfth annual symposium on Computational geometry
Angles of Planar Triangular Graphs
SIAM Journal on Discrete Mathematics
Quasi-greedy triangulations approximating the minimum weight triangulation
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computing Proximity Drawings of Trees in the 3-Dimemsional Space
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Proximity Drawings of Outerplanar Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
Proximity Drawability: a Survey
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Area Requirement of Gabriel Drawings
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Graph Theory With Applications
Graph Theory With Applications
Computational Geometry: Theory and Applications
Polynomial area bounds for MST embeddings of trees
Computational Geometry: Theory and Applications
On the topologies of local minimum spanning trees
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
The three dimensional logic engine
GD'04 Proceedings of the 12th international conference on Graph Drawing
| Hi-index | 5.23 |
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. We study 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 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 not Delaunay drawable - that is, not drawable as a Delaunay triangulatio