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On Cost Allocation in Steiner Tree Networks

  • Chapter
Steiner Trees in Industry

Part of the book series: Combinatorial Optimization ((COOP,volume 11))

Abstract

New technologies prompted an explosion in the development of communication networks. Modern network design techniques often leads to a construction of the most profitable or the least cost network that provides some service to customers. The class of Steiner trees often arises in those considerations. There are various costs and gains associated with building and using Steiner tree networks. Moreover, the involved multiple network users and/or owners possibly have conflicting objectives. However, they might cooperate in order to decrease their joint cost or increase their joint profit. Clearly, these individuals or organizations will support a globally ‘attractive’ solution(s) only if their expectations for a ‘fair share’ of the cost or profit are met. Consequently, providing network developers, users and owners with efficiently computable ‘fair’ cost (profit) allocation solution procedures is of great importance for strategic management. This work is an overview of some results (some previously published as well as some new) in the development of cooperative game theory based mechanisms to efficiently compute ‘attractive’ cost allocation solutions for a class of Steiner tree networks.

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References

  1. Aarts, H., and T. Driessen, A Survey on Minimum on Minimum Cost Spanning Tree Games, Memorandum No. 1003, University of Twente, The Netherlands (1991).

    Google Scholar 

  2. Aneja, Y.P., An Integer Linear Programming Approach to the Steiner Problem in Graphs, Networks, Vol. 10 (1980) 167–178.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Auman and S. Hart, Handbook of Game Theory with Economic Applications, Volume 2, North Holland (1992).

    Google Scholar 

  4. Beasley, J.E., An SST-Based Algorithm for the Steiner Problem in Graphs, Networks, Vol. 19 (1989) 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  5. C. Bird, On Cost Allocation for a Spanning Tree: A Game Theoretic Approach, Networks 6, (1976) 335–350.

    Article  MathSciNet  MATH  Google Scholar 

  6. Chvatal, V., Rational Behavior and Computational Complexity, Technical Report SOCS-78.9, School of Computer Science, McGill University (1978).

    Google Scholar 

  7. Driessen, T., Cooperative Games, Solutions and Applications, Kluwer Academic, Dordrecht, The Netherlands, (1988).

    MATH  Google Scholar 

  8. Dubey P. and L.S. Shapley, Totally Balanced Games Arising from Controlled Programming Problems, Mathematical Programming 29, (1984) 245–267.

    Article  MathSciNet  MATH  Google Scholar 

  9. Edmonds, J., Optimum Branching, National Bureau of Standards Journal of Research 71B, (1967) 233–240.

    MathSciNet  Google Scholar 

  10. Feltkamp, V., S. Tijs and S. Muto, Bird’s Tree Allocation Revisited, Technical Report Center for Econometrics, Tilburg University, March 1994.

    Google Scholar 

  11. Garey, M.R. and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, CA (1979).

    MATH  Google Scholar 

  12. J.R.G. van Gellekom, J.A.M. Potters, Consistent Solution Rules for Standard Tree Enterprises, (1999) to appear in International Journal of Game Theory.

    Google Scholar 

  13. Granot, D., A Generalized Linear Production Model: A Unifying Model, Mathematical Programming 34 (1986), 212–223.

    Article  MathSciNet  MATH  Google Scholar 

  14. Granot, D., The Role of Cost Allocation in Locational Models, Operations Research, Vol. 35, No. 2, (1987) 234–248.

    Article  MathSciNet  MATH  Google Scholar 

  15. Granot, D. and F. Granot, Computational Complexity of a Cost Allocation Approach to a Fixed Cost Spanning Forest Problem, Mathematics of Operations Research, Vol. 17, No. 4, (1992a) 765–780.

    Article  MathSciNet  MATH  Google Scholar 

  16. Granot, D. and G. Huberman, Minimum Cost Spanning Tree Games, Mathematical Programming 21, (1981) 1–18.

    Article  MathSciNet  MATH  Google Scholar 

  17. Granot, D. and G. Huberman, On the Core and Nucleolus of MCST Games, Mathematical Programming 29, (1984) 323–347.

    Article  MathSciNet  MATH  Google Scholar 

  18. Grotte, J.H., Computation of and Observations on the Nucleolus and the Central Games, M.Sc. Thesis, Cornell University, (1970)

    Google Scholar 

  19. Kalai, E. and E. Zemel, Generalized Network Problems Yielding Totally Balanced Games, Operations Research 30, (1982a) 998–1008

    Article  MATH  Google Scholar 

  20. Kent, K., On MCST games, Ph.D. Thesis, Applied Mathematics and Statistics, State University of New York at Stony Brook, (1997).

    Google Scholar 

  21. Kent, K. and D. Skorin-Kapov, Population Monotonic Cost Allocation on MST’s, Operational Research Proceedings KOI’96, (1996) 43–48.

    Google Scholar 

  22. Kent, K. and D. Skorin-Kapov, Distance Monotonic Stable Cost Allocation Scheme for the Minimum Cost Spanning Tree Network, Proceedings of the 19th Conference Information Technology Interfaces ITI’97, (1997) 463–468.

    Google Scholar 

  23. Kolen A., Solving Covering Problems and the Uncapacitated Plant Location Problem on Trees, European Journal of Operational Research 12, (1983) 266–278.

    Article  MathSciNet  MATH  Google Scholar 

  24. Kolen A. and A. Tamir, Covering Problems, Chapter 6 in P.B. Mirchandani and R.L. Francis, eds. Discrete Location Theory, J. Wiley & Sons, Inc. (1990).

    Google Scholar 

  25. Van den Nouweland, A., S. Tijs and M. Maschler, Monotonic Games are spanning Network Games, International Journal of Game Theory 21, (1993) 419–427

    Article  MathSciNet  MATH  Google Scholar 

  26. Owen, G., On the Core of Linear Production Games, Mathematical Programming 9, (1975) 358–370.

    Article  MathSciNet  MATH  Google Scholar 

  27. Owen, G., Game Theory, New York: Academic Press, (1982).

    MATH  Google Scholar 

  28. Preparata, F.P. and M.F. Shamos, Computational Geometry, Wiley (1985).

    Google Scholar 

  29. Prodon, A., M. Liebling and H. Gröflin, “Steiner’s Problem on Two-Trees,“ Working Paper RO 850315, Department of Mathematics, EPF Lausanne, Switzerland, March 1985.

    Google Scholar 

  30. Samet, D. and E. Zemel, On the Core and Dual Set of Linear Programming Games, Mathematics of Operations Research 9, (1984) 309–316

    Article  MathSciNet  MATH  Google Scholar 

  31. Schmeidler, D., The Nucleolus of a Characteristic Function Game, SIAM Journal of Applied Mathematics 17, (1969) 1163–1170.

    Article  MathSciNet  MATH  Google Scholar 

  32. Shapley, L.S. and M. Shubik, The Assignment Game I: The Core, International Journal of Game Theory 1, (1972) 111–130

    Article  MathSciNet  Google Scholar 

  33. Sharkey, W.W., Cores of Games with Fixed Costs and Shared Facilities, International Economic Review 30, (1990) 245 262

    Google Scholar 

  34. Sharkey, W.W., Networks Models in Economics, Bellcore Economics Discussion Paper #69, (1995).

    Google Scholar 

  35. Skorin-Kapov D., A Fixed-Cost Spanning Forest Problem on Series-Parallel Graphs, Proceedings of the 2nd Conference on Operational Research, KOI’92, Rovinj, (1992)

    Google Scholar 

  36. Skorin-Kapov D., On a Cost Allocation Problem Arising From a Capacitated Concentrator Covering Problem, Operations Research Letters, Vol. 13, No. 5, (1993).

    Article  MathSciNet  Google Scholar 

  37. Skorin-Kapov D., On the Core of the Minimum Steiner Tree Game in Networks, Annals of Operations Research, 57 (1995) 233–249.

    Article  MathSciNet  MATH  Google Scholar 

  38. Skorin-Kapov D. and H.F. Beltran, An Efficient Characterization of Cost Allocation Solutions Associated With Capacitated Network Design Problems, Telecommunication Systems, Vol. 3, No. 1, (1994b) 91–107.

    Article  Google Scholar 

  39. Sprumont Y., Population Monotonic Allocation Schemes for Cooperative Games With Transferable Utility, Games and Economic Behavior 2, (1990) 378–394.

    Article  MathSciNet  MATH  Google Scholar 

  40. Tamir A., On the Core of Network Synthesis Games, Mathematical Programming 50, (1991) 123–135

    Article  MathSciNet  MATH  Google Scholar 

  41. Tamir A., On the Core of Cost Allocation Games Defined on Locational Problems, Transportation Science, Vol. 27, No. 1, (1992) 81–86

    Article  MathSciNet  Google Scholar 

  42. S. Voss, Modern Heuristic Search Methods for the Steiner Problem in Graphs, Advances in Steiner Trees, Eds. D-Z Du, J.M. Smith and J.H. Rubinstein, Kluwer Academic Publishers, (2000) 283–323.

    Google Scholar 

  43. Wong, R. T., A Dual Ascent Approach for Steiner Tree Problems on a Directed Graph, Mathematical Programming 28 (1984) 271–287.

    Article  MathSciNet  MATH  Google Scholar 

  44. Young, H.P. (1985), Cost Allocation: Methods, Principles, Applications, North-Holland P.C., Amsterdam.

    Google Scholar 

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Authors and Affiliations

  1. School of Business, Adelphi University, Garden City, NY, 11530, USA

    Darko Skorin-Kapov

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  1. Darko Skorin-Kapov
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, USA

    Xiu Zhen Cheng  & Ding-Zhu Du  & 

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© 2001 Kluwer Academic Publishers

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Skorin-Kapov, D. (2001). On Cost Allocation in Steiner Tree Networks. In: Cheng, X.Z., Du, DZ. (eds) Steiner Trees in Industry. Combinatorial Optimization, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0255-1_11

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  • DOI: https://doi.org/10.1007/978-1-4613-0255-1_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7963-8

  • Online ISBN: 978-1-4613-0255-1

  • eBook Packages: Springer Book Archive

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