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arXiv · 1312.4429

The Flip Diameter of Rectangulations and Convex Subdivisions

Eyal Ackerman·Michelle M. Allen·Gill Barequet·Maarten Löffler·Joshua Mermelstein·Diane L. Souvaine·Csaba D. Tóth
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Abstract

We study the configuration space of rectangulations and convex subdivisions of $n$ points in the plane. It is shown that a sequence of $O(n\log n)$ elementary flip and rotate operations can transform any rectangulation to any other rectangulation on the same set of $n$ points. This bound is the best possible for some point sets, while $\Theta(n)$ operations are sufficient and necessary for others. Some of our bounds generalize to convex subdivisions of $n$ points in the plane.

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Eyal Ackerman, Michelle M. Allen, Gill Barequet, Maarten Löffler, Joshua Mermelstein, Diane L. Souvaine, Csaba D. Tóth. 2013-12-16. The Flip Diameter of Rectangulations and Convex Subdivisions. https://doi.org/10.46298/dmtcs.646

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