Expected wasted space of optimal simple rectangle packing (Q1769075)

Random rectangles are packed in the unit square without overlapping and with the additional property called ``simple'', which means that each vertical line can intersect at most one rectangle. This paper aims at improving the result of \textit{W. T. Rhee} [Ann. Appl. Probab. 10, 539--548 (2000; Zbl 1051.60012)] for the expected waste space of optimal simple rectangle packing in the unit square. The main result states that the expected waste space \(E(W_n)\) (\(n\) being the rectangles packed) satisfies \(\log E(W_n) = -\frac12\log n + \sqrt{\log 2\log n}+O(\log\log n)\).