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Computing an effective decision making group of a society using social network analysis

Author

Listed:
  • Donghyun Kim

    (North Carolina Central University)

  • Deying Li

    (Renmin University of China)

  • Omid Asgari

    (North Carolina Central University)

  • Yingshu Li

    (Georgia State University)

  • Alade O. Tokuta

    (North Carolina Central University)

  • Heekuck Oh

    (Hanyang University)

Abstract

Recent years have witnessed how much a decision making group can be dysfunctional due to the extreme hyperpartisanship. While partisanship is crucial for the representatives to pursue the wishes of those whom they represent for, such an extremism results in a severe gridlock in the decision making progress, and makes themselves highly inefficient. It is known that such a problem can be mitigated by having negotiators in the group. This paper investigates the potential of social network analysis techniques to choose an effective leadership group of a society such that it suffers less from the extreme hyperpartisanship. We establish three essential requirements for an effective representative group, namely Influenceability, Partisanship, and Bipartisanship. Then, we formulate the problem of finding a minimum size representative group satisfying the three requirements as the minimum connected $$k$$ k -core dominating set problem (MC $$k$$ k CDSP), and show its NP-hardness. We introduce an extension of MC $$k$$ k CDSP, namely MC $$k$$ k CDSP-C, which assumes the society has a number of sub-communities and requires at least one representative from each sub-community should be in the leadership. We also propose an approximation algorithm for a subclass of MC $$k$$ k CDSP with $$k=2$$ k = 2 , and show an $$\alpha $$ α -approximation algorithm of MC $$k$$ k CDSP can be used to obtain an $$\alpha $$ α -approximation algorithm of MC $$k$$ k CDSP-SC.

Suggested Citation

  • Donghyun Kim & Deying Li & Omid Asgari & Yingshu Li & Alade O. Tokuta & Heekuck Oh, 2014. "Computing an effective decision making group of a society using social network analysis," Journal of Combinatorial Optimization, Springer, vol. 28(3), pages 577-587, October.
  • Handle: RePEc:spr:jcomop:v:28:y:2014:i:3:d:10.1007_s10878-013-9687-8
    DOI: 10.1007/s10878-013-9687-8
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    References listed on IDEAS

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    1. Kelleher, Laura L. & Cozzens, Margaret B., 1988. "Dominating sets in social network graphs," Mathematical Social Sciences, Elsevier, vol. 16(3), pages 267-279, December.
    2. Xu Zhu & Jieun Yu & Wonjun Lee & Donghyun Kim & Shan Shan & Ding-Zhu Du, 2010. "New dominating sets in social networks," Journal of Global Optimization, Springer, vol. 48(4), pages 633-642, December.
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