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
Computing sums of radicals in polynomial time
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
An O(n2logn) time algorithm for the minmax angle triangulation
SIAM Journal on Scientific and Statistical Computing
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
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Implementations of the LMT heuristic for minimum weight triangulation
Proceedings of the fourteenth annual symposium on Computational geometry
Information Processing Letters
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
A lower bound for &bgr;-skeleton belonging to minimum weight triangulations
Computational Geometry: Theory and Applications
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
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
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
Minimum weight triangulation is NP-hard
Proceedings of the twenty-second annual symposium on Computational geometry
The minimum weight triangulation problem with few inner points
Computational Geometry: Theory and Applications
On minimum weight pseudo-triangulations
Computational Geometry: Theory and Applications
A new asymmetric inclusion region for minimum weight triangulation
Journal of Global Optimization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Algorithms and theory of computation handbook
Residues with Similar Hexagon Neighborhoods Share Similar Side-Chain Conformations
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
SIAM Journal on Computing
On a linear program for minimum-weight triangulation
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Recognizing polar planar graphs using new results for monopolarity
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
The minimum stabbing triangulation problem: IP models and computational evaluation
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
On the Sum of Square Roots of Polynomials and Related Problems
ACM Transactions on Computation Theory (TOCT)
Minimum average distance triangulations
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
The complexity of separating points in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
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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, using a reduction from PLANAR 1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the β-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.