Approximation and Online Algorithms: 12th International by Evripidis Bampis, Ola Svensson

By Evripidis Bampis, Ola Svensson

This publication constitutes the completely refereed post-workshop complaints of the twelfth overseas Workshop on Approximation and on-line Algorithms, WAOA 2014, held in Wrocław, Poland, in September 2014 as a part of ALGO 2014.

The 22 revised complete papers provided have been conscientiously reviewed and chosen from forty nine submissions. They disguise quite a lot of subject matters resembling coloring and partitioning, aggressive research, community layout, packing and protecting, paradigms for layout and research of approximation and on-line algorithms, randomization strategies, real-world functions, and scheduling problems.

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AF algorithms thus open a new bin with an incoming item only when there is no other possibility. Among AF algorithms, First Fit (FF) packs an incoming item into the first bin where it fits (in the order by creation time), Best Fit (BF) chooses the bin with the highest level where the item fits and Worst Fit (WF) packs the item into the bin with the lowest level where it fits. Next Fit (NF) is more restrictive than Any Fit algorithms, since it keeps only a single open bin and puts an incoming item into it whenever the item fits, otherwise the bin is closed and a new one is opened.

In Black and White Bin Packing, when all the items are of size zero, all Any Fit algorithms create a packing into the optimal number of bins [1]. 5. However, in the restricted offline setting a packing into LB2 bins is still always possible, even though this fact is not obvious. This shows that the color discrepancy fully characterizes the combinatorial aspect of the color restriction in Colored Bin Packing. 40 M. B¨ ohm et al. Theorem 1. Let all items have size equal to zero. , items can be packed into LB2 bins without reordering.

If r ≥ 3e, stop the first phase. Assign the current item i according to its item type, using the first possible option in the particular column. The first letter in a cell indicates the required type of the bin before the assignment and the second column denotes the type of the bin after the assignment. If there are two types listed, the new bin type depends on the new size and weight of the bin. Note: As an additional rule when packing regular items, the item is packed in a regular or tiny bin only if the total size packed into this bin does not exceed 6 afterwards.

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