A new asymmetric inclusion region for minimum weight triangulation

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Department of Electrical and Computer Engineering


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 (√ 2 β) -skeleton is a subgraph of a minimum weight triangulation. An algorithm for identifying subgraph of minimum weight triangulation using the one-sided (√ 2 β) -skeleton is proposed and it runs in {O(n4/3+ε+min{κ log n, n 2log n}) time, where κ is the number of intersected segmented between the complete graph and the greedy triangulation of the point set.

Publication Title

Journal of Global Optimization