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Reducing Moser's Square Packing Problem to a Bounded Number of Squares

03/11/2021
by   Meike Neuwohner, et al.
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The problem widely known as Moser's Square Packing Problem asks for the smallest area A such that for any set S of squares of total area 1, there exists a rectangle R of area A into which the squares in S permit an internally-disjoint, axis-parallel packing. It was formulated by Moser in 1966 and remains unsolved so far. The best known lower bound of 2+√(3)/3≤ A is due to Novotný and has been shown to be sufficient for up to 11 squares by Platz, while Hougardy and Ilhan have established that A < 1.37. In this paper, we reduce Moser's Square Packing Problem to a problem on a finite set of squares in the following sense: We show how to compute a natural number N such that it is enough to determine the value of A for sets containing at most N squares with total area 1.

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