Algorithms for core stability, core largeness, exactness, and extendability of flow games

Article

Fang, Qizhi, Fleischer, Rudolf, Li, Jian and Sun, Xiaoxun. 2010. "Algorithms for core stability, core largeness, exactness, and extendability of flow games ." Frontiers of Mathematics in China. 5 (1), pp. 47-63. https://doi.org/10.1007/s11464-009-0048-y
Article Title

Algorithms for core stability, core largeness, exactness, and extendability of flow games

ERA Journal ID32285
Article CategoryArticle
AuthorsFang, Qizhi (Author), Fleischer, Rudolf (Author), Li, Jian (Author) and Sun, Xiaoxun (Author)
Journal TitleFrontiers of Mathematics in China
Journal Citation5 (1), pp. 47-63
Number of Pages17
Year2010
Place of PublicationBeijing, China
ISSN1673-3452
1673-3576
Digital Object Identifier (DOI)https://doi.org/10.1007/s11464-009-0048-y
Web Address (URL)http://www.springerlink.com/content/444828m32402m82r/
Abstract

We study core stability and some related properties of flow games defined on simple networks (all edge capacities are equal) from an algorithmic point of view. We first present a sufficient and necessary condition that can be tested efficiently for a simple flow game to have a stable core. We also prove the equivalence of the properties of core largeness, extendability, and exactness of simple flow games and provide an equivalent graph theoretic characterization which allows us to decide these properties in polynomial time.

Keywordsflow network; series-parallel graph; imputation; cooperative game
ANZSRC Field of Research 2020460609. Networking and communications
461399. Theory of computation not elsewhere classified
360502. Computer gaming and animation
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Byline AffiliationsOcean University of China, China
Fudan University, China
University of Maryland, United States
Department of Mathematics and Computing
Institution of OriginUniversity of Southern Queensland
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