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A Note on Balancedness of Dominating Set Games

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Abstract

In this paper we consider the balancedness of dominating set games, introduced by Velzen 2003. We establish a new kind of 0-1 program formulation to model the domination problem on graphs, and give a strong connection between LP relaxation of this 0-1 program and the cost allocation problem concerning the core of a dominating set game. Duality theory on Lagrange dual is the main technique in our proof. In particular, we use this insight to give the equivalence of the balancedness for two different dominating set games.

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References

  • X. Deng, T. Ibaraki, and H. Nagamochi, “Algorithmic aspects of the core of combinatorial optimization games,” Mathematics of Operations Research, vol. 24, pp. 751–766, 1999.

    MathSciNet  MATH  Google Scholar 

  • U. Faigle and W. Kern, “Partition games and the core of hierarchically convex cost games,” Universiteit Twente, faculteit der toegepaste wiskunde, Memorandum, no. 1269, 1995.

  • M.X. Goemans and M. Skutella, “Cooperative facility location games,” SODA (2000) pp. 76-85, 2000.

  • D. Granot, “A note on the roommate problem and a related revenue allocation problem,” Management Science, vol. 30, pp. 633–643, 1984.

    Article  MATH  Google Scholar 

  • G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization, John Wiley & Sons: New York, 1988.

    MATH  Google Scholar 

  • L.S. Shapley and M. Shubik, “The assignment game,” International Journal of Game Theory, vol. 1, pp. 111–130, 1972.

    MathSciNet  Google Scholar 

  • A. Tamir and J.S.B. Mitchell, “A maximum b-matching problem arising from median location models with applications to the roommate problem,” Mathematical Programming, vol. 80, pp. 171–194, 1998.

    MathSciNet  Google Scholar 

  • B.V. Velzen, “Dominating set game,” CentER Discussion Paper No. 2003-39, Tilbarg University, Center of Economic Research, 2003.

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Authors and Affiliations

  1. Department of Mathematics, Ocean University of China, Qingdao, 266071, P.R. China

    Qizhi Fang

  2. Department of Mathematics, Catholic University of Daegu, Kyungsan, 712-702, Korea

    Hye Kyung Kim

Authors
  1. Qizhi Fang
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  2. Hye Kyung Kim
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Corresponding author

Correspondence to Qizhi Fang.

Additional information

Supported by NSFC (No. 10371114) and KRF-2003-002-C00038

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Fang, Q., Kim, H.K. A Note on Balancedness of Dominating Set Games. J Comb Optim 10, 303–310 (2005). https://doi.org/10.1007/s10878-005-4920-8

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  • DOI: https://doi.org/10.1007/s10878-005-4920-8

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