Bounds on optimally triangulating connected subsets of the minimum weight convex partition
نویسندگان
چکیده
Given a set S of n points, we show that the length of 1) the minimum weight triangulation (MWT ) of the minimum weight convex partition (MWCP ) of S (TMWCP ) is at most Θ(n) longer than the MWT of S if collinearity of two or more edges is allowed and Θ(log n) otherwise, 2) the MWT of the minimum spanning tree (MST ) of the MWCP of S (Tmst(MWCP )) is at most Θ(n) longer than the MWT of S if collinearity of two or more edges is allowed and Θ(log n) otherwise, 3) the MWT of any connected subset G of the MWCP of S (TMWCP (G)) is at most Θ(n) longer than the MWT of S if collinearity of two or more edges is allowed.
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