Frontiers of Mathematics in China

, Volume 5, Issue 1, pp 47–63 | Cite as

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

  • Qizhi Fang
  • Rudolf Fleischer
  • Jian Li
  • Xiaoxun Sun
Research Article

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.

Keywords

Flow network series-parallel graph imputation cooperative game 

MSC

91A12 91A46 05C57 

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Copyright information

© Higher Education Press and Springer Berlin Heidelberg 2009

Authors and Affiliations

  • Qizhi Fang
    • 1
  • Rudolf Fleischer
    • 2
  • Jian Li
    • 3
  • Xiaoxun Sun
    • 4
  1. 1.Department of MathematicsOcean University of ChinaQingdaoChina
  2. 2.Department of Computer Science and EngineeringFudan UniversityShanghaiChina
  3. 3.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
  4. 4.Department of Mathematics and ComputingUniversity of Southern QueenslandToowoombaAustralia

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