By Zhi-Zhong Chen, Ying Fan, Lusheng Wang (auth.), Peter Widmayer, Yinfeng Xu, Binhai Zhu (eds.)

This ebook constitutes the refereed complaints of the seventh foreign convention on Combinatorial Optimization and purposes, COCOA 2013, held in Chengdu, China, in December 2013. The 36 complete papers awarded have been rigorously reviewed and chosen from seventy two submissions. The papers function unique learn within the components of combinatorial optimization and its purposes. as well as theoretical effects there are stories on experimental and utilized learn of basic algorithmic interest.

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Extra resources for Combinatorial Optimization and Applications: 7th International Conference, COCOA 2013, Chengdu, China, December 12-14, 2013, Proceedings

Example text

Zhang time of any surgery cannot be arbitrarily small and is generally less than half of the length of available time interval in a day. We also assume that there is at most one bin open for loading items at any time, that is, the NF rule is adopted during bin packing. Items can be exchanged between an open bin and the buffer during packing. The objective is to minimize the total number of used bins for packing all the released items. We observe that if 1/3 ≤ α < 1/2, then each item is of size within (1/3, 1/2].

Simchi-Levi [5] proved that FF (First Fit) and BF (Best Fit) algorithms have a worst-case ratio of no more than 7/4. Zhang et al. [6] presented a 7/4-competitive online algorithm that runs in linear time and keeps at most four bins open at any time. Some authors studied long term performance of online algorithms which is measured by parameter ACR (asymptotic competitive ratio). We define ACR as follows. For any item input instance σ, let nA (σ), n∗ (σ) be the number of bins used by an online algorithm A and by an optimal offline algorithm OPT respectively.

Go back to Step 1. Step 4. Pack the rest items in S into the current open bin in arbitrary order and close the bin, and finally pack all the rest items in S, if any, into another open bin. Assume that NFB uses totally n bins for any item input instance. By Step 1 of the algorithm, if an item J is packed into Bi in the step, then J is of size not less than any other items in S at the time, which implies that the items in Bi contains the largest items in δi at the beginning of Step 2. Moreover, at each time packing J into Bi in Step 1, the total size of J and the rest items in S is strictly larger than |S| = 1; otherwise J is temporarily stored in the buffer.

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