Abstract

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×(2log⁡5453+2log⁡65)log⁡n+2≈327.1log⁡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 6log⁡nlog⁡97+1≈16.6log⁡n simultaneous flips are sufficient to transform any maximal outerplane graph into any other.

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