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Balancing a Complete Signed Graph by Editing Edges and Deleting Nodes

Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 20)

Abstract

A signed graph is a simple undirected graph in which each edge is either positive or negative. A signed graph is balanced if every cycle has even numbers of negative edges. In this paper we study the problem of balancing a complete signed graph by minimum editing cost, in which the editing operations includes inserting edges, deleting edges, and deleting nodes. We design a branch-and-bound algorithm, as well as a heuristic algorithm. By experimental results we show that the branch-and-bound algorithm is much efficient than a trivial one and the heuristic algorithm performs well.

Keywords

algorithm social network analysis signed graph balanced graph 

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References

  1. 1.
    Böcker, S., Damaschke, P.: Even faster parameterized cluster deletion and cluster editing. Information Processing Letters 111(14), 717–721 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Böcker, S., Briesemeister, S., Bui, Q.B.A., Truss, A.: Going weighted: Parameterized algorithm for cluster editing. Theor. Comput. Sci. 410(52), 5467–5480 (2009)MATHCrossRefGoogle Scholar
  3. 3.
    Chen, J., Meng, J.: A 2k Kernel for the Cluster Editing Problem. In: Thai, M.T., Sahni, S. (eds.) COCOON 2010. LNCS, vol. 6196, pp. 459–468. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Damaschke, P.: Bounded-Degree Techniques Accelerate Some Parameterized Graph Algorithms. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 98–109. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Damaschke, P.: Fixed-parameter enumerability of cluster editing and related problems. Theory Computing Syst. 46, 261–283 (2010)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Fellows, M.R., Guo, J., Komusiewicz, C., Niedermeier, R., Uhlmann, J.: Graph-based data clustering with overlaps. Discrete Optimization 8(1), 2–17 (2011)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: Fixedparameter algorithms for clique generation. Theory Computing Syst. 38, 373–392 (2005)MATHCrossRefGoogle Scholar
  8. 8.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39, 321–347 (2004)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Guo, J.: A more effective linear kernelization for cluster editing. Theor. Comput. Sci. 410, 718–726 (2009)MATHCrossRefGoogle Scholar
  10. 10.
    Harary, F.: On the notion of balance of a signed graph. Michigan Mathematical Journal, 143–146 (1953)Google Scholar
  11. 11.
    Hüffner, F., Komusiewicz, C., Moser, H., Niedermeier, R.: Fixed-parameter algorithms for cluster vertex deletion. Theory of Computing Systems 47(1), 196–217 (2010)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
  13. 13.
    Shamir, R., Sharan, R., Tsur, D.: Cluster Graph Modification Problems. In: Kučera, L. (ed.) WG 2002. LNCS, vol. 2573, pp. 379–390. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press, Cambridge (1994)Google Scholar
  15. 15.
    Wei, P.-S., Wu, B.Y.: Balancing a complete signed graph by changing minimum number of edge signs. In: Proceedings of the 29th Workshop on Combinatorial Mathematics and Computation Theory, Taiwan, (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.National Chung Cheng UniversityChiaYiTaiwan, R.O.C.

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