We consider a variant of the Bin Packing Problem dealing with fragmentable items. Given a fixed number of bins, the objective is to put all the items into the bins by splitting them in a minimum number of fragments. This problem is useful for modeling splittable resource allocation. In this paper we introduce the problem and its complexity then we present a -approximation algorithm for a special case in which all bins have the same capacities.
19 pages, 19 figures, IJCNC, http://airccse.org/journal/cnc/0711cnc13.pdfInternational audienceThe new model that we present in this paper is introduced in the context of guaranteed QoS and resources management in the inter-domain routing framework. This model, called the stock model, is based on a reverse cascade approach and is applied in a distributed context. So transit providers have to learn the right capacities to buy and to stock and, therefore learning theory is applied through an iterative process. We show that transit providers manage to learn how to strategically choose their capacities on each route in order to maximize their benefits, despite the very incomplete information. Finally, we provide and analyse some simulation results given by the application of the model in a simple case where the model quickly converges to a stable state
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