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In the optimal packing, the weight of each bin is at most 17/12; In the First-Fit packing, the average weight of each bin is at least 5/6 = 10/12. Therefore, asymptotically, the number of bins in the FF packing must be at most 17/10 * OPT. For claim 1, it is sufficient to prove that, for any set B with sum at most 1, bonus(B) is at most 5/12 ...
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First-fit-decreasing (FFD) is an algorithm for bin packing. Its input is a list of items of different sizes. Its output is a packing - a partition of the items into bins of fixed capacity, such that the sum of sizes of items in each bin is at most the capacity. Ideally, we would like to use as few bins as possible, but minimizing the number of ...
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Next-k-Fit is a variant of Next-Fit, but instead of keeping only one bin open, the algorithm keeps the last bins open and chooses the first bin in which the item fits. For k ≥ 2 {\displaystyle k\geq 2} , NkF delivers results that are improved compared to the results of NF, however, increasing k {\displaystyle k} to constant values larger than ...
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