Abstract
Given a set of rectangles we are asked to pack as many of them as possible into a bigger rectangle. The rectangles packed may not overlap and may not be rotated. This problem is NP-hard in the strong sense even for packing squares into a square. We establish the relationship between the asymptotic worst-case ratio and the (absolute) worst-case ratio for the problem. It is proved that there exists an asymptotic FPTAS, and thus a PTAS, for packing squares into a rectangle. We give an approximation algorithm with asymptotic ratio of at most two for packing rectangles, and further show a simple (2+ε)-approximation algorithm.
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Jansen, K., Zhang, G. (2004). Maximizing the Number of Packed Rectangles. In: Hagerup, T., Katajainen, J. (eds) Algorithm Theory - SWAT 2004. SWAT 2004. Lecture Notes in Computer Science, vol 3111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27810-8_31
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DOI: https://doi.org/10.1007/978-3-540-27810-8_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22339-9
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