Improved lower bounds for the online bin stretching problem
نویسندگان
چکیده
منابع مشابه
Improved lower bounds for the online bin stretching problem
We use game theory techniques to automatically compute improved lower bounds on the competitive ratio for the bin stretching problem. Using these techniques, we improve the best lower bound for this problem to 19/14. We explain the technique and show that it can be generalized to compute lower bounds for any online or semi-online packing or scheduling problem. We also present a lower bound, wit...
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Online Bin Stretching is a semi-online variant of Bin Packing with a set number of m bins, where all bins can be overpacked to capacity S ≥ 1, which is to be minimized. There is also a guarantee that an offline algorithm can pack the input to m bins of unit size. We focus on the problem of Online Bin Stretching for small m, namely 3 ≤ m ≤ 5. Recent progress on this problem has led into a lower ...
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The bin packing problem has been extensively studied and numerous variants have been considered. The k-item bin packing problem is one of the variants introduced by Krause et al. in Journal of the ACM 22(4). In addition to the formulation of the classical bin packing problem, this problem imposes a cardinality constraint that the number of items packed into each bin must be at most k. For the o...
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We consider several previously studied online variants of bin packing and prove new and improved lower bounds on the asymptotic competitive ratios for them. For that, we use a method of fully adaptive constructions. In particular, we improve the lower bound for the asymptotic competitive ratio of online square packing significantly, raising it from roughly 1.68 to above 1.75.
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Packing a given sequence of items into as few bins as possible in an online fashion is a widely studied problem. We improve lower bounds for packing hypercubes into bins in two or more dimensions, once for general algorithms (in two dimensions) and once for an important subclass, so-called Harmonic-type algorithms (in two or more dimensions). Lastly, we show that two adaptions of the ideas from...
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ژورنال
عنوان ژورنال: 4OR
سال: 2016
ISSN: 1619-4500,1614-2411
DOI: 10.1007/s10288-016-0330-2