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

doi:10.1007/978-3-642-54423-1_42

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: Chapter in Book/Report/Conference proceeding › Conference contribution › 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(nlogn) 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 Θ(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
Title of host publication	LATIN 2014
Subtitle of host publication	Theoretical Informatics - 11th Latin American Symposium, Proceedings
Publisher	Springer Verlag
Pages	478-489
Number of pages	12
ISBN (Print)	9783642544224
DOIs	https://doi.org/10.1007/978-3-642-54423-1_42
State	Published - 2014
Event	11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay Duration: 31 Mar 2014 → 4 Apr 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8392 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th Latin American Theoretical Informatics Symposium, LATIN 2014
Country/Territory	Uruguay
City	Montevideo
Period	31/03/14 → 4/04/14

Bibliographical note

Funding Information:
Löffler is partially supported by the NWO (639.021.123). Allen, Mermelstein, Souvaine, and Tóth are supported in part by the NSF (CCF-0830734).

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-642-54423-1_42

Cite this

Ackerman, E., Allen, M. M., Barequet, G., Löffler, M., Mermelstein, J., Souvaine, D. L., & Tóth, C. D. (2014). The flip diameter of rectangulations and convex subdivisions. In LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings (pp. 478-489). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8392 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-54423-1_42

Ackerman, Eyal ; Allen, Michelle M. ; Barequet, Gill et al. / The flip diameter of rectangulations and convex subdivisions. LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings. Springer Verlag, 2014. pp. 478-489 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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

author = "Eyal Ackerman and Allen, {Michelle M.} and Gill Barequet and Maarten L{\"o}ffler and Joshua Mermelstein and Souvaine, {Diane L.} and T{\'o}th, {Csaba D.}",

note = "Funding Information: L{\"o}ffler is partially supported by the NWO (639.021.123). Allen, Mermelstein, Souvaine, and T{\'o}th are supported in part by the NSF (CCF-0830734).; 11th Latin American Theoretical Informatics Symposium, LATIN 2014 ; Conference date: 31-03-2014 Through 04-04-2014",

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language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Ackerman, E, Allen, MM, Barequet, G, Löffler, M, Mermelstein, J, Souvaine, DL & Tóth, CD 2014, The flip diameter of rectangulations and convex subdivisions. in LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8392 LNCS, Springer Verlag, pp. 478-489, 11th Latin American Theoretical Informatics Symposium, LATIN 2014, Montevideo, Uruguay, 31/03/14. https://doi.org/10.1007/978-3-642-54423-1_42

The flip diameter of rectangulations and convex subdivisions. / Ackerman, Eyal; Allen, Michelle M.; Barequet, Gill et al.
LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings. Springer Verlag, 2014. p. 478-489 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8392 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Souvaine, Diane L.

AU - Tóth, Csaba D.

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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(nlogn) 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 Θ(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(nlogn) 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 Θ(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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Ackerman E, Allen MM, Barequet G, Löffler M, Mermelstein J, Souvaine DL et al. The flip diameter of rectangulations and convex subdivisions. In LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings. Springer Verlag. 2014. p. 478-489. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-54423-1_42

The flip diameter of rectangulations and convex subdivisions

Abstract

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Bibliographical note

ASJC Scopus subject areas

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