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 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.

Bibliographic Details

Main Authors:	Arruda,Vitor Pimenta dos Reis, Mirisola,Luiz Gustavo Bizarro, Soma,Nei Yoshihiro
Format:	Digital revista
Language:	English
Published:	Sociedade Brasileira de Pesquisa Operacional 2022
Online Access:	http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382022000100228
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