Online Knapsack Revisited
We investigate the online variant of the Multiple Knapsack problem: an algorithm is to pack items, of arbitrary sizes and profits, in k knapsacks (bins) without exceeding the capacity of any bin. We study two objective functions: the sum and the maximum of profits over all bins. Both have been studied before in restricted variants of our problem: the sum in Dual Bin Packing , and the maximum in Removable Knapsack [7, 8]. Following these, we study two variants, depending on whether the algorithm is allowed to remove (forever) items from its bins or not, and two special cases where the profit of an item is a function of its size, in addition to the general setting.
We study both deterministic and randomized algorithms; for the latter, we consider both the oblivious and the adaptive adversary model. We classify each variant as either admitting O(1)-competitive algorithms or not. We develop simple O(1)-competitive algorithms for some cases of the max-objective variant believed to be infeasible because only 1-bin deterministic algorithms were considered for them before.
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- 5.Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press (1998)Google Scholar
- 6.Chekuri, C., Gamzu, I.: Truthful mechanisms via greedy iterative packing. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) APPROX and RANDOM 2009. LNCS, vol. 5687, pp. 56–69. Springer, Heidelberg (2009)Google Scholar
- 10.Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack problems. Springer (2004)Google Scholar
- 13.Martello, S., Toth, P.: Knapsack problems. John Wiley & Sons (1990)Google Scholar
- 14.Noga, J., Sarbua, V.: An online partially fractional knapsack problem. In: Proc. of the 8th Int. Symp. on Parallel Architectures, Algorithms, and Networks (ISPAN), pp. 108–112 (2005)Google Scholar
- 15.Sgall, J.: Private communication (2013)Google Scholar