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The Flip Diameter of Rectangulations and Convex Subdivisions

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LATIN 2014: Theoretical Informatics (LATIN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8392))

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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.

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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Author information

Authors and Affiliations

  1. Dept. Math., Physics, and Comp. Sci., University of Haifa at Oranim, Tivon, Israel

    Eyal Ackerman

  2. Department of Computer Science, Tufts University, Medford, MA, USA

    Michelle M. Allen, Joshua Mermelstein & Diane L. Souvaine

  3. Department of Computer Science, Technion, Haifa, Israel

    Gill Barequet

  4. Department of Computing and Information Sciences, Utrecht University, The Netherlands

    Maarten Löffler

  5. Department of Mathematics, California State Univ. Northridge, Los Angeles, CA, USA

    Csaba D. Tóth

Authors
  1. Eyal Ackerman
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  2. Michelle M. Allen
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  3. Gill Barequet
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  4. Maarten Löffler
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  5. Joshua Mermelstein
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  6. Diane L. Souvaine
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  7. Csaba D. Tóth
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Editors and Affiliations

  1. Facultad de Ingeniería, Instituto de Computación, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    Alberto Pardo  & Alfredo Viola  & 

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Ackerman, E. et al. (2014). The Flip Diameter of Rectangulations and Convex Subdivisions. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_42

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  • DOI: https://doi.org/10.1007/978-3-642-54423-1_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54422-4

  • Online ISBN: 978-3-642-54423-1

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