an:01973104
Zbl 1034.68126
Coffman, E. G. jun.; Downey, Peter J.; Winkler, Peter
Packing rectangles in a strip
EN
Acta Inf. 38, No. 10, 673-693 (2002).
00099604
2002
j
68W40 68Q10 90B80
Tetris constraint
Summary: Rectangles with dimensions independently chosen from a uniform distribution on \([0,1]\) are packed on-line into a unit-width strip under a constraint like that of the Tetris\(^{\text{TM}}\) game: rectangles arrive from the top and must be moved inside the strip to reach their place; once placed, they cannot be moved again. Cargo loading applications impose similar constraints. This paper assumes that rectangles must be moved without rotation. For \(n\) rectangles, the resulting packing height is shown to have an asymptotic expected value of at least \((0.31382733\ldots)n\) under any on-line packing algorithm. An on-line algorithm is presented that achieves an asymptotic expected height of \((0.36976421\ldots)n\). This algorithm improves the bound achieved in Next Fit Level (NFL) packing, by compressing the items packed on two successive levels of an NFL packing via on-line movement admissible under the Tetris constraint.