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

Access to Document

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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title = "The flip diameter of rectangulations and convex subdivisions",

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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doi = "10.1007/978-3-642-54423-1\_42",

language = "English",

isbn = "9783642544224",

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 - Löffler, Maarten

AU - Mermelstein, Joshua

AU - Souvaine, Diane L.

AU - Tóth, Csaba D.

N1 - 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).

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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.

UR - https://www.scopus.com/pages/publications/84899917468

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

M3 - Conference contribution

AN - SCOPUS:84899917468

SN - 9783642544224

T3 - 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 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

Access to Document

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