We study the number of simultaneous diagonal flips required to transform any triangulation into any other. The best known algorithm requires no more than $4\times (\frac{2}{\log \frac{54}{53}}+\frac{2}{\log \frac{6}{5}})\log n+2\approx 327.1\log n$ simultaneous flips. This bound is asymptotically tight. In this paper, exploiting some newly discovered properties of blocking and blocked chords we bring the leading constant down to ≈85.8. We also show that $\frac{6\log n}{\log \frac{9}{7}}+1\approx 16.6\log n$ simultaneous flips are sufficient to transform any maximal outerplane graph into any other.

中文翻译：

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通过同时进行对角线翻转来转换平面三角剖分

我们研究了将任何三角剖分转换为其他三角剖分所需的同时对角翻转的次数。最著名的算法只需要$4\times （\frac{\mathrm{2个}}{\mathrm{日志}\frac{54}{53}}+\frac{\mathrm{2个}}{\mathrm{日志}\frac{6}{5}}）\mathrm{日志}ñ+\mathrm{2个}\approx 327.1\mathrm{日志}ñ$同时翻转。这个界限是渐近严格的。在本文中，我们利用阻塞和和弦的一些新发现的属性，将前导常数降至≈85.8。我们还表明$\frac{6\mathrm{日志}ñ}{\mathrm{日志}\frac{9}{7}}+\mathrm{1个}\approx 16.6\mathrm{日志}ñ$ 同时翻转足以将任何最大外平面图转换成任何其他外平面图。