Finding nucleolus of flow game

Deng, Xiaotie and Fang, Qizhi and Sun, Xiaoxun (2009) Finding nucleolus of flow game. Journal of Combinatorial Optimization , 18 (1). pp. 64-86. ISSN 1382-6905

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 N℘-hard for flow games with general capacity.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to published version due to publisher copyright policy.
Depositing User: epEditor USQ
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 08 Dec 2011 11:26
Last Modified: 03 Jul 2013 00:57
Uncontrolled Keywords: efficient algorithm; flow game; linear program duality; N℘-hard; nucleolus; maximum flows
Fields of Research (FOR2008): 08 Information and Computing Sciences > 0805 Distributed Computing > 080503 Networking and Communications
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080201 Analysis of Algorithms and Complexity
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970108 Expanding Knowledge in the Information and Computing Sciences
Identification Number or DOI: doi: 10.1007/s10878-008-9138-0
URI: http://eprints.usq.edu.au/id/eprint/20375

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