The Flip Diameter of Rectangulations and Convex Subdivisions

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...

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Bibliographic Details
Published in:	Discrete mathematics and theoretical computer science Vol. 18 no. 3; no. Combinatorics
Main Authors:	Ackerman, Eyal, Allen, Michelle M., Barequet, Gill, Löffler, Maarten, Mermelstein, Joshua, Souvaine, Diane L., Tóth, Csaba D.
Format:	Journal Article
Language:	English
Published:	Discrete Mathematics & Theoretical Computer Science 17.03.2016
Subjects:	computer science - computational geometry computer science - discrete mathematics mathematics - combinatorics
ISSN:	1365-8050, 1365-8050
Online Access:	Get full text
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Summary:	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.
ISSN:	1365-8050 1365-8050
DOI:	10.46298/dmtcs.646