Finding nucleolus of flow game

Xiaotie Deng, Qizhi Fang () and Xiaoxun Sun
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Xiaotie Deng: City University of Hong Kong
Qizhi Fang: Ocean University of China
Xiaoxun Sun: University of Southern Queensland

Journal of Combinatorial Optimization, 2009, vol. 18, issue 1, No 5, 64-86

Abstract: 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.

Keywords: Flow game; Nucleolus; Linear program duality; Efficient algorithm; $\mathcal{NP}$ -hard (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10878-008-9138-0

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