Abstract
We present a \(1-\frac{1}{\sqrt{k}}\)-competitive algorithm for the online stochastic generalized assignment problem under the assumption that no item takes up more than \(\frac{1}{k}\) fraction of the capacity of any bin. Items arrive online; each item has a value and a size; upon arrival, an item can be placed in a bin or discarded; the objective is to maximize the total value of the placement. Both value and size of an item may depend on the bin in which the item is placed; the size of an item is revealed only after it has been placed in a bin; distribution information is available about the value and size of each item in advance (not necessarily i.i.d), however items arrive in adversarial order (non-adaptive adversary).
We also present an application of our result to subscription-based advertising where each advertiser, if served, requires a given minimum number of impressions (i.e., the “all or nothing” model).
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Alaei, S., Hajiaghayi, M., Liaghat, V. (2013). The Online Stochastic Generalized Assignment Problem. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2013 2013. Lecture Notes in Computer Science, vol 8096. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40328-6_2
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DOI: https://doi.org/10.1007/978-3-642-40328-6_2
Publisher Name: Springer, Berlin, Heidelberg
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