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

Paper

Fang, Qizhi, Fleischer, Rudolf, Li, Jian and Sun, Xiaoxun. 2007. "Algorithms for core stability, core largeness, exactness, and extendability of flow games ." Lin, G. (ed.) COCOON 2007: 13th Annual International Computing and Combinatorics Conference. Banff, Canada 16 - 19 Jul 2007 Berlin, Germany. https://doi.org/10.1007/978-3-540-73545-8_43
Paper/Presentation Title

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

Presentation TypePaper
AuthorsFang, Qizhi (Author), Fleischer, Rudolf (Author), Li, Jian (Author) and Sun, Xiaoxun (Author)
EditorsLin, G.
Journal or Proceedings TitleLecture Notes in Computer Science (Book series)
Journal Citation4598, pp. 439-447
Number of Pages9
Year2007
PublisherSpringer
Place of PublicationBerlin, Germany
ISSN1611-3349
0302-9743
ISBN9783540735441
Digital Object Identifier (DOI)https://doi.org/10.1007/978-3-540-73545-8_43
Web Address (URL) of Paperhttp://www.springerlink.com/content/pg4473643h383731/?MUD=MP
Conference/EventCOCOON 2007: 13th Annual International Computing and Combinatorics Conference
Event Details
COCOON 2007: 13th Annual International Computing and Combinatorics Conference
Event Date
16 to end of 19 Jul 2007
Event Location
Banff, Canada
Abstract

In this paper, we give linear time algorithms to decide core
stability, core largeness, exactness, and extendability of flow games on uniform networks (all edge capacities are 1). We show that a uniform flow game has a stable core if and only if the network is a balanced DAG (for all non-terminal vertices, indegree equals outdegree), which can be decided in linear time. Then we show that uniform flow games are exact, extendable, and have a large core if and only if the network is a balanced directed series-parallel graph, which again can be decided in linear time.

Keywordsalgorithms; computer graphics; linear programming; flow games; linear time algorithms; game theory
ANZSRC Field of Research 2020490302. Numerical analysis
461399. Theory of computation not elsewhere classified
460702. Computer graphics
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Byline AffiliationsOcean University of China, China
Fudan University, China
Department of Mathematics and Computing
Institution of OriginUniversity of Southern Queensland
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