Voronoi diagrams and arrangements
Discrete & Computational Geometry
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Realizability of Delaunay triangulations
Information Processing Letters
Toughness and Delaunay triangulations
Discrete & Computational Geometry
Lower bounds for algebraic computation trees with integer inputs
SIAM Journal on Computing
A general approach to dominance in the plane
Journal of Algorithms
Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Simpler proof of a realizability theorem on Delaunay triangulations
Information Processing Letters
Graph-theoretical conditions for inscribability and Delaunay realizability
Discrete Mathematics
An optimal algorithm for realizing a Delaunay triangulation
Information Processing Letters
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Computational Geometry: Theory and Applications
Certifying algorithms for recognizing interval graphs and permutation graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Determining the Separation of Preprocessed Polyhedra - A Unified Approach
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Proximity Drawability: a Survey
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Proximity Constraints and Representable Trees
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Competitive facility location: the Voronoi game
Theoretical Computer Science
Graphs and Digraphs, Fourth Edition
Graphs and Digraphs, Fourth Edition
Efficient algorithms for bichromatic separability
ACM Transactions on Algorithms (TALG)
Covering the Convex Quadrilaterals of Point Sets
Graphs and Combinatorics
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Approximate proximity drawings
GD'11 Proceedings of the 19th international conference on Graph Drawing
Blocking Delaunay triangulations
Computational Geometry: Theory and Applications
Approximate proximity drawings
Computational Geometry: Theory and Applications
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Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural way of implicitly representing graphs. However, as a tool for graph representation, proximity graphs have some limitations that may be overcome with suitable generalizations. We introduce a generalization, witness graphs, that encompasses both the goal of more power and flexibility for graph drawing issues and a wider spectrum for neighborhood analysis. We study in detail two concrete examples, both related to Delaunay graphs, and consider as well some problems on stabbing geometric objects and point set discrimination, that can be naturally described in terms of witness graphs.