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


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.


Planar Graph Relative Interior Vertical Segment Horizontal Segment Operation Rotate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Eyal Ackerman
    • 1
  • Michelle M. Allen
    • 2
  • Gill Barequet
    • 3
  • Maarten Löffler
    • 4
  • Joshua Mermelstein
    • 2
  • Diane L. Souvaine
    • 2
  • Csaba D. Tóth
    • 5
  1. 1.Dept. Math., Physics, and Comp. Sci.University of Haifa at OranimTivonIsrael
  2. 2.Department of Computer ScienceTufts UniversityMedfordUSA
  3. 3.Department of Computer ScienceTechnionHaifaIsrael
  4. 4.Department of Computing and Information SciencesUtrecht UniversityThe Netherlands
  5. 5.Department of MathematicsCalifornia State Univ. NorthridgeLos AngelesUSA

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