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Algorithms for Core Stability, Core Largeness, Exactness, and Extendability of Flow Games

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Computing and Combinatorics (COCOON 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4598))

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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.

The work described in this paper was supported by NCET, NSFC (No. 10371114s and No. 70571040/G0105) and partially supported by NSFC (No. 60573025).

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Authors and Affiliations

  1. Department of Mathematics, Ocean University of China, Qingdao, China

    Qizhi Fang

  2. Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China

    Rudolf Fleischer & Jian Li

  3. Department of Mathematics and Computing, University of Southern Queensland,  

    Xiaoxun Sun

Authors
  1. Qizhi Fang
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  2. Rudolf Fleischer
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  3. Jian Li
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  4. Xiaoxun Sun
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Editor information

Guohui Lin

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Fang, Q., Fleischer, R., Li, J., Sun, X. (2007). Algorithms for Core Stability, Core Largeness, Exactness, and Extendability of Flow Games. In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_43

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  • DOI: https://doi.org/10.1007/978-3-540-73545-8_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73544-1

  • Online ISBN: 978-3-540-73545-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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