A Greedy Approximation Algorithm for the Multi-dimensional Minimum Knapsack Problem
نویسندگان
چکیده
We consider the minimization version of the multi-dimensional knapsack problem with bounded integer variables. We propose a greedy approximation algorithm that runs in O(mn) time and has a guarantee of m + 1, where n is the number of items and m is the number of knapsack constraints. The guarantee of the algorithm can be improved in case of easy coefficients in the constraints associated with some of the dimensions. As a consequence, we show that the greedy is a 2-approximation algorithm for the multiple choice minimization knapsack problem. Finally, using filtering based on the greedy algorithm and LP rounding, we improve the guarantee bounds.
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