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Efficient Generation of Rectangulations via Permutation Languages

Authors Arturo Merino , Torsten Mütze



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Author Details

Arturo Merino
  • TU Berlin, Germany
Torsten Mütze
  • University of Warwick, Coventry, United Kingdom
  • Charles University, Prague, Czech Republic

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Arturo Merino and Torsten Mütze. Efficient Generation of Rectangulations via Permutation Languages. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 54:1-54:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.SoCG.2021.54

Abstract

A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a large variety of different classes of generic rectangulations. Our algorithms work under very mild assumptions, and apply to a large number of rectangulation classes known from the literature, such as generic rectangulations, diagonal rectangulations, 1-sided/area-universal, block-aligned rectangulations, and their guillotine variants. They also apply to classes of rectangulations that are characterized by avoiding certain patterns, and in this work we initiate a systematic investigation of pattern avoidance in rectangulations. Our generation algorithms are efficient, in some cases even loopless or constant amortized time, i.e., each new rectangulation is generated in constant time in the worst case or on average, respectively. Moreover, the Gray codes we obtain are cyclic, and sometimes provably optimal, in the sense that they correspond to a Hamilton cycle on the skeleton of an underlying polytope. These results are obtained by encoding rectangulations as permutations, and by applying our recently developed permutation language framework.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Mathematics of computing → Discrete mathematics
Keywords
  • Exhaustive generation
  • Gray code
  • flip graph
  • polytope
  • generic rectangulation
  • diagonal rectangulation
  • cartogram
  • floorplan
  • permutation pattern

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