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An FPTAS for Stochastic Unbounded Min-Knapsack Problem

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Frontiers in Algorithmics (FAW 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11458))

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Abstract

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 Min-SUKP 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 Min-SUKP, 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 \((1+\epsilon )\) times the optimum, and our algorithm runs in \(poly(1/\epsilon ,n,\log W)\) time.

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Acknowledgement

The authors would like to thank Jian Li for several useful discussions and the help with polishing the paper. The research is supported in part by the National Basic Research Program of China Grant 2015CB358700, the National Natural Science Foundation of China Grant 61822203, 61772297, 61632016, 61761146003, and a grant from Microsoft Research Asia.

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Authors and Affiliations

  1. Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China

    Zhihao Jiang & Haoyu Zhao

Authors
  1. Zhihao Jiang
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  2. Haoyu Zhao
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Correspondence to Zhihao Jiang or Haoyu Zhao .

Editor information

Editors and Affiliations

  1. Fudan University, Shanghai, China

    Yijia Chen

  2. Peking University, Beijing, China

    Xiaotie Deng

  3. Tsinghua University, Beijing, China

    Mei Lu

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Jiang, Z., Zhao, H. (2019). An FPTAS for Stochastic Unbounded Min-Knapsack Problem. In: Chen, Y., Deng, X., Lu, M. (eds) Frontiers in Algorithmics. FAW 2019. Lecture Notes in Computer Science(), vol 11458. Springer, Cham. https://doi.org/10.1007/978-3-030-18126-0_11

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  • DOI: https://doi.org/10.1007/978-3-030-18126-0_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-18125-3

  • Online ISBN: 978-3-030-18126-0

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