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Finding nucleolus of flow game

Author

Listed:
  • Xiaotie Deng

    (City University of Hong Kong)

  • Qizhi Fang

    (Ocean University of China)

  • Xiaoxun Sun

    (University of Southern Queensland)

Abstract

We study the algorithmic issues of finding the nucleolus of a flow game. The flow game is a cooperative game defined on a network D=(V,E;ω). The player set is E and the value of a coalition S⊆E is defined as the value of a maximum flow from source to sink in the subnetwork induced by S. We show that the nucleolus of the flow game defined on a simple network (ω(e)=1 for each e∈E) can be computed in polynomial time by a linear program duality approach, settling a twenty-three years old conjecture by Kalai and Zemel. In contrast, we prove that both the computation and the recognition of the nucleolus are $\mathcal{NP}$ -hard for flow games with general capacity.

Suggested Citation

  • Xiaotie Deng & Qizhi Fang & Xiaoxun Sun, 2009. "Finding nucleolus of flow game," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 64-86, July.
    • Handle: RePEc:spr:jcomop:v:18:y:2009:i:1:d:10.1007_s10878-008-9138-0
    DOI: 10.1007/s10878-008-9138-0
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    References listed on IDEAS

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    Cited by:

    1. Qizhi Fang & Bo Li & Xiaohan Shan & Xiaoming Sun, 2018. "Path cooperative games," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 211-229, July.
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    3. Serap Ergün & Pınar Usta & Sırma Zeynep Alparslan Gök & Gerhard Wilhelm Weber, 2023. "A game theoretical approach to emergency logistics planning in natural disasters," Annals of Operations Research, Springer, vol. 324(1), pages 855-868, May.
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    5. Vijay V. Vazirani, 2023. "LP-Duality Theory and the Cores of Games," Papers 2302.07627, arXiv.org, revised Mar 2023.
    6. Sergei Dotsenko & Vladimir Mazalov, 2021. "A Cooperative Network Packing Game with Simple Paths," Mathematics, MDPI, vol. 9(14), pages 1-18, July.

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