Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the two-dimensional bin packing problem: Given a list of n rectangles the objective is to find a feasible, i.e. axis-parallel and non-overlapping, packing of all rectangles into the minimum number of unit sized squares, also called bins. Our problem consists of two versions; in the first version it is not allod to rotate the rectangles while in the other it is allod to rotate the rectangles by 90°, i.e. to exchange the widths and the heights.#R##N##R##N#Two-dimensional bin packing is a generalization of its one-dimensional counterpart and is therefore strongly NP-hard. Furthermore Bansal et al. [2] shod that even an APTAS is ruled out for this problem, unless P = NP. This lor bound of asymptotic approximability was improved by Chlebik & Chlebikova [4] to values 1 + 1/3792 and 1 + 1/2196 for the version with and without rotations, respectively. On the positive side there is an asymptotic 1.69.. approximation by Caprara [3] without rotations and an asymptotic 1.52... approximation by Bansal et al. [1] for both versions.#R##N##R##N# give a new asymptotic upper bound for both versions of our problem: For any fixed e and any instance that fits optimally into OPT bins, our algorithm computes a packing into (1.5+ e) OPT+ 69 bins with polynomial running time in the input length.#R##N##R##N#In our new technique  consider an optimal packing of the rectangles into the bins.  cut a small vertical or horizontal strip out of each bin and move the intersecting rectangles into additional bins. This enables us to either round the widths of all wide rectangles, or the heights of all long rectangles in this bin. After this step  round the other, unrounded side of these rectangles and  achieve a solution with a simple structure and only few types of rectangles. Our algorithm initially rounds the instance and computes a solution that nearly matches the modified optimal solution.
['Klaus Jansen', 'Lars Prädel']
I am writing a research paper on a idea New approximability results for two-dimensional bin packing
[{"from": "human", "value": "I am writing a research paper on a idea New approximability results for two-dimensional bin packing"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the two-dimensional bin packing problem: Given a list of n rectangles the objective is to find a feasible, i.e. axis-parallel and non-overlapping, packing of all rectangles into the minimum number of unit sized squares, also called bins. Our problem consists of two versions; in the first version it is not allod to rotate the rectangles while in the other it is allod to rotate the rectangles by 90\u00b0, i.e. to exchange the widths and the heights.#R##N##R##N#Two-dimensional bin packing is a generalization of its one-dimensional counterpart and is therefore strongly NP-hard. Furthermore Bansal et al. [2] shod that even an APTAS is ruled out for this problem, unless P = NP. This lor bound of asymptotic approximability was improved by Chlebik & Chlebikova [4] to values 1 + 1/3792 and 1 + 1/2196 for the version with and without rotations, respectively. On the positive side there is an asymptotic 1.69.. approximation by Caprara [3] without rotations and an asymptotic 1.52... approximation by Bansal et al. [1] for both versions.#R##N##R##N# give a new asymptotic upper bound for both versions of our problem: For any fixed e and any instance that fits optimally into OPT bins, our algorithm computes a packing into (1.5+ e) OPT+ 69 bins with polynomial running time in the input length.#R##N##R##N#In our new technique  consider an optimal packing of the rectangles into the bins.  cut a small vertical or horizontal strip out of each bin and move the intersecting rectangles into additional bins. This enables us to either round the widths of all wide rectangles, or the heights of all long rectangles in this bin. After this step  round the other, unrounded side of these rectangles and  achieve a solution with a simple structure and only few types of rectangles. Our algorithm initially rounds the instance and computes a solution that nearly matches the modified optimal solution."}]