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On the Complexity of Testing Membership in the Core of Min-Cost Spanning Tree Games

Author

Listed:
  • 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)

  • Winfried Hochstättler

    (ZPR, Zentrum für paralleles Rechnen Universität zu Köln Albertus-Magnus-Platz, H 50923 Köln, Germany)

  • Sándor P. Fekete

    (ZPR, Zentrum für paralleles Rechnen Universität zu Köln Albertus-Magnus-Platz, H 50923 Köln, Germany)

Abstract

Let $N=\{ 1,...,n\} $ be a finite set of players and $K_{N}$ the complete graph on the node set $N\cup \{ 0\} $. Assume that the edges of $K_{N}$ have nonnegative weights and associate with each coalition $S\subseteq N$ of players as cost $c(S)$ the weight of a minimal spanning tree on the node set $S\cup \{ 0\} $. Using transformation from EXACT COVER BY 3-SETS, we exhibit the following problem to be NP-complete. Given the vector $x\in R^{N}$ with $x(N)=c(N)$. Decide whether there exists a coalition S such that $x(S) > c(S)$.

Suggested Citation

  • Ulrich Faigle & Walter Kern & Winfried Hochstättler & Sándor P. Fekete, 1997. "On the Complexity of Testing Membership in the Core of Min-Cost Spanning Tree Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 361-366.
    • Handle: RePEc:spr:jogath:v:26:y:1997:i:3:p:361-366
    Note: Received May 1995 Revised version I May 1996 Revised version II June 1996
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    Citations

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    Cited by:

    1. Xin Chen & Jiawei Zhang, 2009. "A Stochastic Programming Duality Approach to Inventory Centralization Games," Operations Research, INFORMS, vol. 57(4), pages 840-851, August.
    2. 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.
    3. 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.
    4. Phuoc Hoang Le & Tri-Dung Nguyen & Tolga Bektaş, 2016. "Generalized minimum spanning tree games," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(2), pages 167-188, May.
    5. Ulrich Faigle & Walter Kern & Jeroen Kuipers, 2006. "Computing an Element in the Lexicographic Kernel of a Game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 427-433, July.
    6. 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.
    7. Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
    8. Darko Skorin-Kapov, 2018. "Social enterprise tree network games," Annals of Operations Research, Springer, vol. 268(1), pages 5-20, September.

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