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A Note on Balancedness of Dominating Set Games

Author

Listed:
  • Qizhi Fang

    (Ocean University of China)

  • Hye Kyung Kim

    (Catholic University of Daegu)

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.

Suggested Citation

  • Qizhi Fang & Hye Kyung Kim, 2005. "A Note on Balancedness of Dominating Set Games," Journal of Combinatorial Optimization, Springer, vol. 10(4), pages 303-310, December.
    • Handle: RePEc:spr:jcomop:v:10:y:2005:i:4:d:10.1007_s10878-005-4920-8
    DOI: 10.1007/s10878-005-4920-8
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    References listed on IDEAS

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    1. Daniel Granot, 1984. "A Note on the Room-Mates Problem and a Related Revenue Allocation Problem," Management Science, INFORMS, vol. 30(5), pages 633-643, May.
    2. GOEMANS, Michel X. & SKUTELLA, Martin, 2000. "Cooperative facility location games," LIDAM Discussion Papers CORE 2000014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Xiaotie Deng & Toshihide Ibaraki & Hiroshi Nagamochi, 1999. "Algorithmic Aspects of the Core of Combinatorial Optimization Games," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 751-766, August.
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