Abstract.
We study the d-dimensional knapsack problem in the data streaming model. The knapsack is modelled as a d-dimensional integer vector of capacities. For simplicity, we assume that the input is scaled such that all capacities are 1. There is an input stream of n items, each item is modelled as a d-dimensional integer column of non-negative inte- ger weights and a scalar pro_t. The input instance has to be processed in an online fashion using sub-linear space. After the items have arrived, an approximation for the cost of an optimal solution as well as a template for an approximate solution is output. Our algorithm achieves an approximation ratio (2( 1 2+ q 2d + 1 4 ))