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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| Vydané v: | Discrete mathematics and theoretical computer science Ročník 18 no. 3; číslo Combinatorics |
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| Hlavní autori: | , , , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Discrete Mathematics & Theoretical Computer Science
17.03.2016
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| ISSN: | 1365-8050, 1365-8050 |
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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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Ackerman, Eyal Löffler, Maarten Allen, Michelle M. Barequet, Gill Mermelstein, Joshua Souvaine, Diane L. Tóth, Csaba D. |
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| Snippet | 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... 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... |
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| Title | The Flip Diameter of Rectangulations and Convex Subdivisions |
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