ALMOST SQUARING THE SQUARE: OPTIMAL PACKINGS FOR NON-DECOMPOSABLE SQUARES

ABSTRACT We consider the problem of finding the minimum uncovered area (trim loss) when tiling non- overlapping distinct integer-sided squares in an N × N square container such that the squares are placed with their edges parallel to those of the container. We find such trim losses and associated op...

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Bibliographic Details
Published in:Pesquisa Operacional 2022, Vol.42
Main Authors: Arruda, Vitor Pimenta dos Reis, Mirisola, Luiz Gustavo Bizarro, Soma, Nei Yoshihiro
Format: Article
Language:English
Subjects:
OPERATIONS RESEARCH & MANAGEMENT SCIENCE
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Summary:ABSTRACT We consider the problem of finding the minimum uncovered area (trim loss) when tiling non- overlapping distinct integer-sided squares in an N × N square container such that the squares are placed with their edges parallel to those of the container. We find such trim losses and associated optimal packings for all container sizes N from 1 to 101, through an independently developed adaptation of Ian Gambini’s enumerative algorithm. The results were published as a new sequence to The On-Line Encyclopedia of Integer Sequences®. These are the first known results for optimal packings in non-decomposable squares.
ISSN:0101-7438
1678-5142
1678-5142
DOI:10.1590/0101-7438.2022.042.00262876