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Next-fit is an online 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 bins is an ...
Best-fit is an online 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 bins is an ...
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 ...
Open a new empty bin, bin #1. 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.
Initialize an empty bin and call it the "open bin". For each item in order, check if it can fit into the open bin: If it fits, then place the new item into it. Otherwise, close the current bin, open a new bin, and put the current item inside it. In short: NFD orders the items by descending size, and then calls next-fit bin packing.
Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, people are given: A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers ...
Bin-packing with fragmentation or fragmentable object bin-packing is a variant of the bin packing problem in which it is allowed to break items into parts and put each part separately on a different bin. Breaking items into parts may allow for improving the overall performance, for example, minimizing the number of total bin.
This problem is a dual of the bin packing problem: in bin covering, the bin sizes are bounded from below and the goal is to maximize their number; in bin packing, the bin sizes are bounded from above and the goal is to minimize their number. [1] The problem is NP-hard, but there are various efficient approximation algorithms: