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Network strength games: the core and the nucleolus

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Abstract

The maximum number of edge-disjoint spanning trees in a network has been used as a measure of the strength of a network. It gives the number of disjoint ways that the network can be fully connected. This suggests a game theoretic analysis that shows the relative importance of the different links to form a strong network. We introduce the Network strength game as a cooperative game defined on a graph \(G=(V,E)\). The player set is the edge-set E and the value of a coalition \(S \subseteq E\) is the maximum number of disjoint spanning trees included in S. We study the core of this game, and we give a polynomial combinatorial algorithm to compute the nucleolus when the core is non-empty.

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Acknowledgements

We are grateful to both referees. Their comments helped us to improve the presentation.

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Authors and Affiliations

  1. CNRS, and Université Clermont II, Campus des cézeaux, BP 125, 63173, Aubière cedex, France

    Mourad Baïou

  2. IBM T. J. Watson Research Center, Yorktown Heights, NY, 10589, USA

    Francisco Barahona

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  1. Mourad Baïou
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  2. Francisco Barahona
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Correspondence to Francisco Barahona.

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Baïou, M., Barahona, F. Network strength games: the core and the nucleolus. Math. Program. 180, 117–136 (2020). https://doi.org/10.1007/s10107-018-1348-3

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  • DOI: https://doi.org/10.1007/s10107-018-1348-3

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