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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Vydáno v:	Discrete mathematics and theoretical computer science Ročník 18 no. 3; číslo Combinatorics
Hlavní autoři:	Ackerman, Eyal, Allen, Michelle M., Barequet, Gill, Löffler, Maarten, Mermelstein, Joshua, Souvaine, Diane L., Tóth, Csaba D.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Discrete Mathematics & Theoretical Computer Science 17.03.2016
Témata:	computer science - computational geometry computer science - discrete mathematics mathematics - combinatorics
ISSN:	1365-8050, 1365-8050
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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