An ω(√n) lower bound for the nonoptimality of the greedy triangulation
Information Processing Letters
A heuristic triangulation algorithm
Journal of Algorithms
Which triangulations approximate the complete graph?
Proceedings of the international symposium on Optimal algorithms
The problem of compatible representatives
SIAM Journal on Discrete Mathematics
Polynomial-time instances of the minimum weight triangulation problem
Computational Geometry: Theory and Applications
Computing a subgraph of the minimum weight triangulation
Computational Geometry: Theory and Applications
The extensible drawing editor Ipe
Proceedings of the eleventh annual symposium on Computational geometry
Approaching the largest &bgr;-skeleton within a minimum weight triangulation
Proceedings of the twelfth annual symposium on Computational geometry
On computing edges that are in all minimum-weight triangulations
Proceedings of the twelfth annual symposium on Computational geometry
Approximation algorithms for geometric problems
Approximation algorithms for NP-hard problems
Implementations of the LMT heuristic for minimum weight triangulation
Proceedings of the fourteenth annual symposium on Computational geometry
Quasi-greedy triangulations approximating the minimum weight triangulation
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
On exclusion regions for optimal triangulations
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Branch-and-Cut Approach for Minimum Weight Triangulation
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
A Chain Decomposition Algorithm for the Proof of a Property on Minimum Weight Triangulations
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Diamonds Are Not a Minimum Weight Triangulation's Best Friend
Proceedings of the 8th Canadian Conference on Computational Geometry
ACM Transactions on Algorithms (TALG)
A quasi-polynomial time approximation scheme for minimum weight triangulation
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A quasi-polynomial time approximation scheme for minimum weight triangulation
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A linear time algorithm for max-min length triangulation of a convex polygon
Information Processing Letters
Minimum weight pseudo-triangulations
Computational Geometry: Theory and Applications
Minimum-weight triangulation is NP-hard
Journal of the ACM (JACM)
Minimum weight convex Steiner partitions
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Decomposing a simple polygon into pseudo-triangles and convex polygons
Computational Geometry: Theory and Applications
A fixed parameter algorithm for optimal convex partitions
Journal of Discrete Algorithms
A quasi-polynomial time approximation scheme for minimum weight triangulation
Journal of the ACM (JACM)
Optimal higher order Delaunay triangulations of polygons
Computational Geometry: Theory and Applications
Optimization for first order Delaunay triangulations
Computational Geometry: Theory and Applications
An incremental algorithm for distributed minimum weight triangulation
PDCN '08 Proceedings of the IASTED International Conference on Parallel and Distributed Computing and Networks
Technical Section: Parallel GPU-based data-dependent triangulations
Computers and Graphics
Computing geometric minimum-dilation graphs is NP-hard
GD'06 Proceedings of the 14th international conference on Graph drawing
Optimal higher order Delaunay triangulations of polygons
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Use of the TRIPOD overlay network for resource discovery
Future Generation Computer Systems
Inapproximability for planar embedding problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Beyond triangulation: covering polygons with triangles
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Fundamenta Informaticae - Emergent Computing
Optimization for first order delaunay triangulations
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard. We use a reduction from PLANAR-1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using geometric inclusion and exclusion criteria for MWT edges, such as the diamond test and the LMT-Skeleton heuristic, as well as dynamic programming on polygonal faces.