Packing into the smallest square: Worst-case analysis of lower bounds

Authors:
Alberto Caprara;Andrea Lodi;Silvano Martello;Michele Monaci
Affiliations:
DEIS, Universití di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy;DEIS, Universití di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy;DEIS, Universití di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy;DEI, Universití di Padova, Via Gradenigo 6/A, I-35131 Padova, Italy
Venue:
Discrete Optimization
Year:
2006

Citing 7
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Abstract

We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90^@?. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature.