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Note Computing the nucleolus of min-cost spanning tree games is NP-hard

Author

Listed:
  • Jeroen Kuipers

    (Instituto de Economia Publica, Universidad del Pais Vasco, Avda. Lehen-Dakari Aguirre 83, E-48015 Bilbao, Spain)

  • Ulrich Faigle

    (Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands)

  • Walter Kern

    (Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands)

Abstract

We prove that computing the nucleolus of minimum cost spanning tree games is in general NP-hard. The proof uses a reduction from minimum cover problems.

Suggested Citation

  • Jeroen Kuipers & Ulrich Faigle & Walter Kern, 1998. "Note Computing the nucleolus of min-cost spanning tree games is NP-hard," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 443-450.
    • Handle: RePEc:spr:jogath:v:27:y:1998:i:3:p:443-450
    Note: Received October 1997/Final version May 1998
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    Citations

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    Cited by:

    1. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
    2. Sanjith Gopalakrishnan & Daniel Granot & Frieda Granot, 2021. "Consistent Allocation of Emission Responsibility in Fossil Fuel Supply Chains," Management Science, INFORMS, vol. 67(12), pages 7637-7668, December.
    3. Qizhi Fang & Bo Li & Xiaohan Shan & Xiaoming Sun, 2018. "Path cooperative games," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 211-229, July.
    4. Balázs Sziklai & Tamás Fleiner & Tamás Solymosi, 2014. "On the Core of Directed Acyclic Graph Games," CERS-IE WORKING PAPERS 1418, Institute of Economics, Centre for Economic and Regional Studies.
    5. Sung, Shao-Chin & Dimitrov, Dinko, 2010. "Computational complexity in additive hedonic games," European Journal of Operational Research, Elsevier, vol. 203(3), pages 635-639, June.
    6. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    7. F.Javier Martínez-de-Albéniz & Carles Rafels & Neus Ybern, 2015. "Insights into the nucleolus of the assignment game," UB School of Economics Working Papers 2015/333, University of Barcelona School of Economics.
    8. Tamas Solymosi & Balazs Sziklai, 2015. "Universal Characterization Sets for the Nucleolus in Balanced Games," CERS-IE WORKING PAPERS 1512, Institute of Economics, Centre for Economic and Regional Studies.
    9. Xiaotie Deng & Qizhi Fang & Xiaoxun Sun, 2009. "Finding nucleolus of flow game," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 64-86, July.
    10. repec:has:discpr:1321 is not listed on IDEAS
    11. Walter Kern & Daniël Paulusma, 2003. "Matching Games: The Least Core and the Nucleolus," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 294-308, May.
    12. Gustavo Bergantiños & Juan Vidal-Puga, 2021. "A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 73-100, March.
    13. Walter Kern & Daniël Paulusma, 2009. "On the Core and f -Nucleolus of Flow Games," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 981-991, November.

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    Keywords

    Nucleolus ·;

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