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Register a new userAn FPTAS for Stochastic Unbounded Min-Knapsack Problem
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Added by
Zhihao Jiang
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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In this paper, we study the stochastic unbounded min-knapsack problem ($textbf{Min-SUKP}$). 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 prob~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 prob, different types of items may have different cost and weight distributions. In this paper, we provide an FPTAS for $textbf{Min-SUKP}$, i.e., the approximate value our algorithm computes is at most $(1+epsilon)$ times the optimum, and our algorithm runs in $poly(1/epsilon,n,log W)$ time.
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We consider the distributed version of the Multiple Knapsack Problem (MKP), where $m$ items are to be distributed amongst $n$ processors, each with a knapsack. We propose different distributed approximation algorithms with a tradeoff between time and message complexities. The algorithms are based on the greedy approach of assigning the best item to the knapsack with the largest capacity. These algorithms obtain a solution with a bound of $frac{1}{n+1}$ times the optimum solution, with either $mathcal{O}left(mlog nright)$ time and $mathcal{O}left(m nright)$ messages, or $mathcal{O}left(mright)$ time and $mathcal{O}left(mn^{2}right)$ messages.
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