Computational geometry: an introduction
Computational geometry: an introduction
Realizability of Delaunay triangulations
Information Processing Letters
Toughness and Delaunay triangulations
Discrete & Computational Geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
The realization problem for Euclidean minimum spanning trees is NP-hard
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Drawing outerplanar minimum weight triangulations
Information Processing Letters
Handbook of discrete and computational geometry
Triangulations without minimum-weight drawing
Information Processing Letters
The drawability problem for minimum weight triangulations
Theoretical Computer Science
Computing Proximity Drawings of Trees in the 3-Dimemsional Space
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
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
Trees with convex faces and optimal angles
GD'06 Proceedings of the 14th international conference on Graph drawing
Computational Geometry: Theory and Applications
The three dimensional logic engine
GD'04 Proceedings of the 12th international conference on Graph Drawing
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We study the problem of characterizing sets of points whose Voronoi diagrams are trees and if so, what are the combinatorial properties of these trees. The second part of the problem can be naturally turned into the following graph drawing question: Given a tree T, can one represent T so that the resulting drawing is a Voronoi diagram of some set of points? We investigate the problem both in the Euclidean and in the Manhattan metric. The major contributions of this paper are as follows. • We characterize those trees that can be drawn as Voronoi diagrams in the Euclidean metric. • We characterize those sets of points whose Voronoi diagrams are trees in the Manhattan metric. • We show that the maximum vertex degree of any tree that can be drawn as a Manhattan Voronoi diagram is at most five and prove that this bound is tight. • We characterize those binary trees that can be drawn as Manhattan Voronoi diagrams.