An Integer Linear Programming Model for Tilings

In this paper, we propose an Integer Linear Model whose solutions are the aperiodic rhythms tiling with a given rhythm A. We show how this model can be used to efficiently check the necessity of the Coven-Meyerowitz's \((T2)\) condition and also to define an iterative algorithm that finds all t...

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Bibliographic Details
Published inarXiv.org
Main Authors Auricchio, Gennaro, Ferrarini, Luca, Lanzarotto, Greta
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.07.2021
Subjects
Integer programming
Iterative algorithms
Iterative methods
Linear programming
Rhythm
Tiling
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Summary:In this paper, we propose an Integer Linear Model whose solutions are the aperiodic rhythms tiling with a given rhythm A. We show how this model can be used to efficiently check the necessity of the Coven-Meyerowitz's \((T2)\) condition and also to define an iterative algorithm that finds all the possible tilings of the rhythm A. To conclude, we run several experiments to validate the time efficiency of this model.
ISSN:2331-8422