There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
Delaunay graphs are almost as good as complete graphs
Discrete & Computational Geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Image synthesis from a sparse set of views
VIS '97 Proceedings of the 8th conference on Visualization '97
Implementations of the LMT heuristic for minimum weight triangulation
Proceedings of the fourteenth annual symposium on Computational geometry
Constant-Time Algorithms for Constrained Triangulations on Reconfigurable Meshes
IEEE Transactions on Parallel and Distributed Systems
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
The Delauney Triangulation Closely Approximates the Complete Euclidean Graph
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Tools for Triangulations and Tetrahedrizations
Scientific Visualization, Overviews, Methodologies, and Techniques
The complexity of combinatorial optimization problems.
The complexity of combinatorial optimization problems.
How to Solve It: Modern Heuristics
How to Solve It: Modern Heuristics
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Analysis of Variance of Cross-Validation Estimators of the Generalization Error
The Journal of Machine Learning Research
Experimental Research in Evolutionary Computation: The New Experimentalism (Natural Computing Series)
Geometric Spanner Networks
Statistical Comparisons of Classifiers over Multiple Data Sets
The Journal of Machine Learning Research
Computing a minimum-dilation spanning tree is NP-hard
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
Optimal Triangulation in 3D Computer Vision Using a Multi-objective Evolutionary Algorithm
Proceedings of the 2007 EvoWorkshops 2007 on EvoCoMnet, EvoFIN, EvoIASP,EvoINTERACTION, EvoMUSART, EvoSTOC and EvoTransLog: Applications of Evolutionary Computing
Computing geometric minimum-dilation graphs is NP-hard
GD'06 Proceedings of the 14th international conference on Graph drawing
Improved upper bound on the stretch factor of delaunay triangulations
Proceedings of the twenty-seventh annual symposium on Computational geometry
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The complexity status of the minimum dilation triangulation (MDT) problem for a general point set is unknown. Therefore, we focus on the development of approximated algorithms to find high quality triangulations of minimum dilation. For an initial approach, we design a greedy strategy able to obtain approximate solutions to the optimal ones in a simple way. We also propose an operator to generate the neighborhood which is used in different algorithms: Local Search, Iterated Local Search, and Simulated Annealing. Besides, we present an algorithm called Random Local Search where good and bad solutions are accepted using the previous mentioned operator. For the experimental study we have created a set of problem instances since no reference to benchmarks for these problems were found in the literature. We use the sequential parameter optimization toolbox for tuning the parameters of the SA algorithm. We compare our results with those obtained by the OV-MDT algorithm that uses the obstacle value to sort the edges in the constructive process. This is the only available algorithm found in the literature. Through the experimental evaluation and statistical analysis, we assess the performance of the proposed algorithms using this operator.