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

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

Faculty of Natural Sciences

Research output: Contribution to journal › Article › peer-review

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 T(n) operations are sufficient and necessary for others. Some of our bounds generalize to convex subdivisions of n points in the plane.

Original language	English
Article number	4
Journal	Discrete Mathematics and Theoretical Computer Science
Volume	18
Issue number	3
State	Published - 2016

Bibliographical note

Publisher Copyright:
© 2016 by the author(s).

Keywords

Combinatorial geometry
Rectangulation

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)
Discrete Mathematics and Combinatorics

Cite this

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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 T(n) operations are sufficient and necessary for others. Some of our bounds generalize to convex subdivisions of n points in the plane.",

keywords = "Combinatorial geometry, Rectangulation",

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AU - Ackerman, Eyal

AU - Allen, Michelle M.

AU - Barequet, Gill

AU - Löffler, Maarten

AU - Mermelstein, Joshua

AU - Souvaine, Diane L.

AU - Tóth, Csaba D.

PY - 2016

Y1 - 2016

N2 - 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 T(n) operations are sufficient and necessary for others. Some of our bounds generalize to convex subdivisions of n points in the plane.

AB - 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 T(n) operations are sufficient and necessary for others. Some of our bounds generalize to convex subdivisions of n points in the plane.

KW - Combinatorial geometry

KW - Rectangulation

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