An FPTAS for Stochastic Unbounded Min-Knapsack Problem
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In this paper, we study the stochastic unbounded min-knapsack problem (Min-SUKP). The ordinary unbounded min-knapsack problem states that: There are n types of items, and there is an infinite number of items of each type. The items of the same type have the same cost and weight. We want to choose a set of items such that the total weight is at least W and the total cost is minimized. The generalizes the ordinary unbounded min-knapsack problem to the stochastic setting, where the weight of each item is a random variable following a known distribution and the items of the same type follow the same weight distribution. In , different types of items may have different cost and weight distributions. In this paper, we provide an FPTAS for Min-SUKP, i.e., the approximate value our algorithm computes is at most (1+ϵ) times the optimum, and our algorithm runs in poly(1/ϵ,n, W) time.
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