Two-dimensional bin packing with one-dimensional resource augmentation

نویسندگان

Nikhil Bansal

Maxim Sviridenko

چکیده

The 2-dimensional Bin Packing problem is a generalization of the classical Bin Packing problems and is defined as follows: Given a collection of rectangles specified by their width and height, the goal is to pack these into minimum number of square bins of unit size. Recently, the problem was proved to be APX-hard even in the asymptotic case, i.e. when the optimum solutions requires a large number of bins [1]. On the positive side, there exists a polynomial time algorithm that uses OPT bins whose sides have length (1 + ǫ), where OPT denotes the number of unit bins used by the optimum solution[1]. A natural question that remains is approximability of the problem when we are allowed to relax the size of the unit bins in only one dimension. In this paper, we show that there exists an asymptotic polynomial time approximation scheme for packing rectangles into bins of size 1× (1 + ǫ).

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