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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.
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 respectively.
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.
First-fit-decreasing bin packing; H. ... Next-fit-decreasing bin packing This page was last edited on 4 October 2021, at 22:20 (UTC). Text is available under the ...
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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The best-fit algorithm uses the following heuristic: It keeps a list of open bins, which is initially empty. When an item arrives, it finds the bin with the maximum load into which the item can fit, if any. The load of a bin is defined as the sum of sizes of existing items in the bin before placing the new item.