Abstract
We consider the problem of packing a set of weighted rectangles into a unit size square frame [0,1] × [0,1] so as to maximize the total weight of the packed rectangles. We present polynomial time approximation schemes (PTASs) that, for any ε>0, find (1 - ε)-approximate solutions for two special cases of the problem. In the first case we pack a set of squares whose weights are equal to their areas. In the second case we pack a set of weighted rectangles into an augmented square frame [0,1 + 3ε] × [0,1 + 3ε].
Supported by EU-Project CRESCCO “Critical Resource Sharing for Cooperation in Complex Systems”, IST-2001-33135.
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© 2005 Springer-Verlag Berlin Heidelberg
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Fishkin, A.V., Gerber, O., Jansen, K., Solis-Oba, R. (2005). Packing Weighted Rectangles into a Square. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_31
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DOI: https://doi.org/10.1007/11549345_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28702-5
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