, Volume 46, Issue 1, pp 63-73
Date: 28 Feb 2009

A new asymmetric inclusion region for minimum weight triangulation

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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.