On the complexity of testing membership in the core of min-cost spanning tree games (original) (raw)

Abstract

Let_N_ = {1,...,n} be a finite set of players and_K_ N the complete graph on the node set_N_∪{0}. Assume that the edges of_K_ N have nonnegative weights and associate with each coalition_S_∪N of players as cost_c_(S) the weight of a minimal spanning tree on the node set_S_∪{0}.

Using transformation from EXACT COVER BY 3-SETS, we exhibit the following problem to be_NP_-complete. Given the vector_x_εℜitN with_x_(N) =c(N). decide whether there exists a coalition_S_ such that_x_(S) >c(S).

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References

  1. Aarts H [1994] Minimum cost spanning tree games and set games. Ph.D. Thesis, University of Twente, Endschede
    Google Scholar
  2. Aarts H, Driessen TSH [1993] The irreducible core of a minimum cost spanning tree game. Zeitschrift für Operations Research 38: 163–174
    Google Scholar
  3. Bird C [1976] On cost allocation for a spanning tree: A game theoretic approach. Networks 6: 335–350
    Google Scholar
  4. Chvátal V [1978] Rational behavior and computational complexity. Technical Report SOCS-78.9, School of Computer Science, McGill University, Montreal
    Google Scholar
  5. Claus A, Kleitman DJ [1973] Cost allocation for a spanning tree. Networks 3: 289–304
    Google Scholar
  6. Deng X, Papadimitriou CH [1994] On the complexity of cooperative solution concepts. Mathematics of Operations Research 19: 257–266
    Google Scholar
  7. Edmonds J [1970] Submodular functions, matroids, and certain polyhedra. In: Guy R. et al. (eds.) Combinatorial structures and their applications. Gordon and Breach, New York: 69–87
    Google Scholar
  8. Garey MR, Johnson DS [1979] Computers and intractability. A guide to the theory of NP-completeness. Freeman, New York
    Google Scholar
  9. Grötschel M, Lovász L, Schrijver A [1988] Geometric algorithms and combinatorial optimization. Springer-Verlag, Berlin
    Google Scholar
  10. Granot D, Granot F [1993] Computational complexity of a cost allocation approach to a fixed cost spanning forest problem. Mathematics of Operations Research 17: 765–780
    Google Scholar
  11. Granot D, Huberman G [1981] Minimum cost spanning tree games. mathematical Programming 21: 1–18
    Google Scholar
  12. Granot D, Huberman G [1982] The relationship between convex games and minimum cost spanning tree games: A case for permutationally convex games. SIAM Journ. Algebraic and Discrete Methods 3: 288–292
    Google Scholar
  13. Kuipers J [1994] Combinatorial methods in cooperative game theory. Ph.D. Thesis, University of Limburg, Maastricht
    Google Scholar
  14. Meggido N [1978] Computational complexity of the game theory approach to cost allocation for a tree. Mathematics of Operations Research 3: 189–196
    Google Scholar
  15. Shapley LS [1971] Cores and convex games. International Journal of Game Theory 1: 1–26
    Google Scholar
  16. Tamir A [1991] On the core of network synthesis games. Mathematical Programming 50: 123–135
    Google Scholar

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500, AE Enschede, The Netherlands
    Ulrich Faigle & Walter Kern
  2. ZPR, Zentrum für paralleles Rechnen Universität zu Köln Albertus-Magnus-Platz, H 50923, Köln, Germany
    Sándor P. Fekete & Winfried Hochstättler

Authors

  1. Ulrich Faigle
  2. Walter Kern
  3. Sándor P. Fekete
  4. Winfried Hochstättler

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Faigle, U., Kern, W., Fekete, S.P. et al. On the complexity of testing membership in the core of min-cost spanning tree games.Int J Game Theory 26, 361–366 (1997). https://doi.org/10.1007/BF01263277

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