Abstract
In this paper, we prove a tight bound for β value \( \left( {\beta = \frac{{\sqrt {2\sqrt 3 + 9} }} {3}} \right) \) ) 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(n 2 log n) time.
This work is partially supported by NSERC grant OPG0041629.
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Wang, C.A., Yang, B. (1999). A Tight Bound for β-Skeleton of Minimum Weight Triangulations. In: Dehne, F., Sack, JR., Gupta, A., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1999. Lecture Notes in Computer Science, vol 1663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48447-7_27
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DOI: https://doi.org/10.1007/3-540-48447-7_27
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