Annals of Operations Research

, Volume 271, Issue 2, pp 831–851 | Cite as

Minimum tiling of a rectangle by squares

  • Michele MonaciEmail author
  • André Gustavo dos Santos
Original Research


We consider a two-dimensional problem in which one is required to split a given rectangular bin into the smallest number of items. The resulting items must be squares to be packed, without overlapping, into the bin so as to cover all the given rectangle. We present a mathematical model and a heuristic algorithm that is proved to find the optimal solution in some special cases. Then, we introduce a relaxation of the problem and present different exact approaches based on this relaxation. Finally, we report computational experiments on the performances of the algorithms on a large set of randomly generated instances.


Two-dimensional packing Mathematical models Exact algorithms Computational experiments 



This research was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil under Grant PVE 030479/2013-01. Thanks are due to an anonymous referee for helpful comments.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.DEIUniversità di BolognaBolognaItaly
  2. 2.DPIUniversidade Federal de ViçosaViçosaBrazil

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