Computing the minimum weight triangulation of a set of linearly ordered points
Information Processing Letters
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
A better subgraph of the minimum weight triangulation
Information Processing Letters
Approaching the largest &bgr;-skeleton within a minimum weight triangulation
Proceedings of the twelfth annual symposium on Computational geometry
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
On Stable Line Segments in Triangulations
Proceedings of the 8th Canadian Conference on Computational Geometry
Diamonds Are Not a Minimum Weight Triangulation's Best Friend
Proceedings of the 8th Canadian Conference on Computational Geometry
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In this paper, we prove a tight bound for β value (β =√2√3+9/3 ) such that being less than this value, the β-skeleton of a planar point set may not belong to the minimum weight triangulation of this set, while being equal to or greater than this value, the β-skeleton always belongs to the minimum weight triangulation. Thus, we settled the conjecture of the tight bound for β-skeleton of minimum weight triangulation by Mark Keil. We also present a new sufficient condition for identifying a subgraph of minimum weight triangulation of a planar n-point set. The identified subgraph could be different from all the known subgraphs, and the subgraph can be found in O(n2log n) time.