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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Article number4
JournalDiscrete Mathematics and Theoretical Computer Science
Volume18
Issue number3
StatePublished - 2016

Bibliographical note

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

Keywords

  • Combinatorial geometry
  • Rectangulation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Discrete Mathematics and Combinatorics

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