On packing squares into a rectangle (Q634254)

A well-known question by Moser (1966) asks for the smallest number \(A\) such that any set of squares with total area \(1\) can be packed into some rectangle of area \(A\), where the squares and rectangle must be axis-parallel. The first bounds on \(A\) were obtained by Moon and Moser in 1967, showing that \(1.2<A<2\). Several improvements have been obtained subsequently, and in the paper under review the author improves the upper bound to \(2867/2048=1.399\dots\). Via a classical result of \textit{A. Meir} and \textit{L. Moser}, J. Comb. Theory 5, 126--134 (1968; Zbl 0165.25202)], the problem is reduced to a finite number of packing problems which are successfully treated by a computer program. In particular, this approach leads to a linear time algorithm for finding such a packing.