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For each item from largest to smallest, find the first bin into which the item fits, if any. If such a bin is found, put the new item in it. Otherwise, open a new empty bin put the new item in it. In short: FFD orders the items by descending size, and then calls first-fit bin packing. An equivalent description of the FFD algorithm is as follows.
The first-fit algorithm uses the following heuristic: It keeps a list of open bins, which is initially empty. When an item arrives, find the first bin into which the item can fit, if any. If such a bin is found, the new item is placed inside it. Otherwise, a new bin is opened and the coming item is placed inside it.
Therefore, Next-Fit-Increasing has the same performance as Next-Fit-Decreasing. [26] Modified first-fit-decreasing (MFFD) [27], improves on FFD for items larger than half a bin by classifying items by size into four size classes large, medium, small, and tiny, corresponding to items with size > 1/2 bin, > 1/3 bin, > 1/6 bin, and smaller items ...
First-fit bin packing; First-fit-decreasing bin packing; H. ... Next-fit-decreasing bin packing This page was last edited on 4 October 2021, at 22:20 (UTC). ...
The algorithm uses as a subroutine, an algorithm called first-fit-decreasing bin packing (FFD). The FFD algorithm takes as input the same set S of numbers, and a bin-capacity c. It heuristically packs numbers into bins such that the sum of numbers in each bin is at most C, aiming to use as few bins as possible.
The Best Fit Decreasing and First Fit Decreasing strategies use no more than 11/9 OPT + 1 bins (where OPT is the number of bins given by the optimal solution). I think this needs a citation. Worst-Case Performance Bounds for Simple One-Dimensional Packing Algorithms only proves 11/9 OPT + 4.
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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 ...