Probabilistic Analysis of Online (Class-Constrained) Bin Packing and Bin Covering
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We study online algorithms for bin packing and bin covering in two different probabilistic settings in which the item sizes are drawn randomly or the items are adversarial but arrive in random order. We prove several results on the expected performance of well-known online algorithms in these settings. In particular, we prove that the simple greedy algorithm Dual Next-Fit for bin covering performs in the random-order setting strictly better than in the worst case, proving a conjecture by Christ et al. (Theoret Comput Sci 556:71–84, 2014).
Additionally we also study class-constrained bin packing and bin covering. In these problems, each item has not only a size but also a color and there are constraints on the number of different colors in each bin. These problems have been studied before in the classical worst-case model and we provide the first probabilistic analysis of these problems. We prove for several simple online algorithms bounds on their expected performance in the two probabilistic models discussed above. We observe that in the case of class constrained bin packing for several algorithms their performance differs with respect to the two probabilistic performance measures.
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