Abstract
As a global optimization problem, planar minimum weight triangulation problem has attracted extensive research attention. In this paper, a new asymmetric graph called one-sided β-skeleton is introduced. We show that the one-sided circle-disconnected \({(\sqrt{2}\beta)}\) -skeleton is a subgraph of a minimum weight triangulation. An algorithm for identifying subgraph of minimum weight triangulation using the one-sided \({(\sqrt{2}\beta)}\) -skeleton is proposed and it runs in \({O(n^{4/3+\epsilon}+\min\{\kappa \log n, n^2\log n\})}\) time, where κ is the number of intersected segmented between the complete graph and the greedy triangulation of the point set.
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Hu, S. A new asymmetric inclusion region for minimum weight triangulation. J Glob Optim 46, 63–73 (2010). https://doi.org/10.1007/s10898-009-9409-z
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DOI: https://doi.org/10.1007/s10898-009-9409-z