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algorithms, such as Next Fit, First Fit or Best are actually used. It is also conceivable that this approach is of interest for offline bin packing. The best practical algorithm for offline bin packing is Best-fit-decreasing (BFD), in which the Best fit algorithm is applied to the items,

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competitive ratios. Forexample, Next Fit (NF)for colorful bin packing (and for black and white bin packing) packs items into a single active bin, and moves to a new active bin as soon as packing an item into the active bin is impossible. For standard bin packing, a new active bin is opened when there is no space for the new

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Program to Implement the Bin Packing Algorithm This is a sample program to illustrate the Bin-Packing algorithm using next fit heuristics. In the bin packing problem, objects of different volumes must be packed into a finite number of bins or containers each of volume V in a way that minimizes the number of bins used.

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In fact there is indeed a packing needing only two bins: Bin 1: 8, 8, 4 and Bin 2: 10, 7, 3. In this notation the item of weight 8 is at the bottom of Bin 1, next comes the item of weight 8, and the item of size 4 occupies the space at the top of the bin. Note that this solution is not unique because the items within the bin can be permuted.

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The next-fit algorithm's output is at most twice the sum of sizes of items plus 1. This gives us an asymptotic 2-approx algorithm for 1D bin-packing.

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Kim and J. Wy, Last two fit augmentation to the well-known construction heuristics for one dimensional bin packing problem: an empirical study, International Journal Advanced Manufacturing Technology, Volume 50, pp. 1145– 1152 (2010).

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