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Journal of Computer Science and Technology

, Volume 33, Issue 4, pp 823–837 | Cite as

A Two-Player Coalition Cooperative Scheme for the Bodyguard Allocation Problem

  • José Alberto Fernández-Zepeda
  • Daniel Brubeck-Salcedo
  • Daniel Fajardo-Delgado
  • Héctor Zatarain-Aceves
Regular Paper
  • 15 Downloads

Abstract

We address the bodyguard allocation problem (BAP), an optimization problem that illustrates the conflict of interest between two classes of processes with contradictory preferences within a distributed system. While a class of processes prefers to minimize its distance to a particular process called the root, the other class prefers to maximize it; at the same time, all the processes seek to build a communication spanning tree with the maximum social welfare. The two state-of-the-art algorithms for this problem always guarantee the generation of a spanning tree that satisfies a condition of Nash equilibrium in the system; however, such a tree does not necessarily produce the maximum social welfare. In this paper, we propose a two-player coalition cooperative scheme for BAP, which allows some processes to perturb or break a Nash equilibrium to find another one with a better social welfare. By using this cooperative scheme, we propose a new algorithm called FFC-BAPS for BAP. We present both theoretical and empirical analyses which show that this algorithm produces better quality approximate solutions than former algorithms for BAP.

Keywords

bodyguard allocation problem coalitional game graph algorithm Nash equilibrium 

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References

  1. [1]
    Tanenbaum A S, van Steen M. Distributed Systems: Principles and Paradigms (2nd edition). Prentice-Hall, Inc., 2006.Google Scholar
  2. [2]
    Nisan N, Roughgarden T, Tardos É, Vazirani V V. Algorithmic Game Theory. Cambridge University Press, 2007.Google Scholar
  3. [3]
    Halpern J Y. Beyond Nash equilibrium: Solution concepts for the 21st century. In Proc. the 27th ACM Symp. Principles of Distributed Computing, August 2008.Google Scholar
  4. [4]
    Manshaei M H, Zhu Q Y, Alpcan T, Bacşar T, Hubaux J P. Game theory meets network security and privacy. ACM Computing Surveys, 2013, 45(3): Article No. 25.Google Scholar
  5. [5]
    Feldman M, Lai K, Stoica I, Chuang J. Robust incentive techniques for peer-to-peer networks. In Proc. the 5th ACM Conf. Electronic Commerce, May 2004, pp.102-111.Google Scholar
  6. [6]
    Feldman M, Papadimitriou C, Chuang J, Stoica I. Freeriding and whitewashing in peer-to-peer systems. IEEE Journal on Selected Areas in Communications, 2006, 24(5): 1010-1019.CrossRefGoogle Scholar
  7. [7]
    Roughgarden T. Selfish Routing and the Price of Anarchy. The MIT Press, 2005.Google Scholar
  8. [8]
    Koutsoupias E, Papadimitriou C. Worst-case equilibria. Computer Science Review, 2009, 3(2): 65-69.CrossRefzbMATHGoogle Scholar
  9. [9]
    von Neumann J, Morgenstern O. Theory of Games and Economic Behavior. Princeton University Press, 2007.Google Scholar
  10. [10]
    Fajardo-Delgado D, Fernández-Zepeda J A, Bourgeois A G. The bodyguard allocation problem. IEEE Trans. Parallel and Distributed Systems, 2013, 24(7): 1465-1478.CrossRefGoogle Scholar
  11. [11]
    Nash J F Jr. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America, 1950, 36(1): 48-49.Google Scholar
  12. [12]
    Dasgupta A, Ghosh S, Tixeuil S. Selfish stabilization. In Stabilization, Safety, and Security of Distributed Systems, Datta A K, Datta M (eds.), Springer, 2006, pp.231-243.Google Scholar
  13. [13]
    Cohen J, Dasgupta A, Ghosh S, Tixeuil S. An exercise in selfish stabilization. ACM Trans. Autonomous and Adaptive Systems, 2008, 3(4): Article No. 15.Google Scholar
  14. [14]
    Zatarain-Aceves H, Fernández-Zepeda J A, Brizuela C A, Fajardo-Delgado D. A cascade evolutionary algorithm for the bodyguard allocation problem. Applied Soft Computing, 2015, 37: 643-651.CrossRefGoogle Scholar
  15. [15]
    Raidl G R, Julstrom B A. Edge sets: An effective evolutionary coding of spanning trees. IEEE Trans. Evolutionary Computation, 2003, 7(3): 225-239.CrossRefGoogle Scholar
  16. [16]
    Barabási A L, Albert R. Emergence of scaling in random networks. Science, 1999, 286(5439): 509-512.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Erdös P, Rényi A. On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci., 1960, 5: 17-61.Google Scholar
  18. [18]
    Kumar R, Raghavan P, Rajagopalan S, Sivakumar D, Tomkins A, Upfal E. Stochastic models for the web graph. In Proc. the 41st Annual Symp. Foundations of Computer Science, November 2000, pp.57-65.Google Scholar
  19. [19]
    Schulz A S, Moses N S. On the performance of user equilibria in traffic networks. In Proc. the 14th Annual ACMSIAM Symp. Discrete Algorithms, January 2003, pp.86-87.Google Scholar
  20. [20]
    Anshelevich E, Dasgupta A, Kleinberg J, Tardos E, Wexler T, Roughgarden T. The price of stability for network design with fair cost allocation. In Proc. the 45th Annual IEEE Symp. Foundations of Computer Science, October 2004, pp.295-304.Google Scholar
  21. [21]
    Blum C, Roli A. Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Computing Surveys, 2003, 35(3): 268-308.CrossRefGoogle Scholar
  22. [22]
    Eiben A E, Jelasity M. A critical note on experimental research methodology in EC. In Proc. Congress on Evolutionary Computation, May 2002, pp.582-587.Google Scholar
  23. [23]
    Črepinšek M, Liu S H, Mernik M. Replication and comparison of computational experiments in applied evolutionary computing: Common pitfalls and guidelines to avoid them. Applied Soft Computing, 2014, 19: 161-170.CrossRefGoogle Scholar
  24. [24]
    Lilliefors H W. On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 1967, 62(318): 399-402.CrossRefGoogle Scholar
  25. [25]
    Conover WJ. Practical Nonparametric Statistics.Wiley Series in Probability and Statistics, John Wiley & Sons, 1980.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • José Alberto Fernández-Zepeda
    • 1
  • Daniel Brubeck-Salcedo
    • 1
  • Daniel Fajardo-Delgado
    • 2
  • Héctor Zatarain-Aceves
    • 1
  1. 1.Department of Computer Science, Center for Scientific Research and Higher Education of EnsenadaEnsenadaMexico
  2. 2.Department of Systems and ComputationInstituto Technológico de Ciudad GuzmánGuzmánMexico

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