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Optimal Edge Deletions for Signed Graph Balancing

  • Falk Hüffner
  • Nadja Betzler
  • Rolf Niedermeier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4525)

Abstract

The Balanced Subgraph problem (edge deletion variant) asks for a 2-coloring of a graph that minimizes the inconsistencies with given edge labels. It has applications in social networks, systems biology, and integrated circuit design. We present an exact algorithm for Balanced Subgraph based on a combination of data reduction rules and a fixed-parameter algorithm. The data reduction is based on finding small separators and a novel gadget construction scheme. The fixed-parameter algorithm is based on iterative compression with a very effective heuristic speedup. Our implementation can solve biological real-world instances exactly for which previously only approximations [DasGupta et al. WEA 2006] were known.

Keywords

Cost Vector Edge Deletion Methanosarcina Barkeri Extra Vertex Separator Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Avidor, A., Langberg, M.: The multi-multiway cut problem. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 273–284. Springer, Heidelberg (2004)Google Scholar
  2. Chiang, C., Kahng, A.B., Sinha, S., Xu, X., Zelikovsky, A.Z.: Fast and efficient bright-field AAPSM conflict detection and correction. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 26(1), 115–126 (2007)CrossRefGoogle Scholar
  3. DasGupta, B., Enciso, G.A., Sontag, E.D., Zhang, Y.: Algorithmic and complexity results for decompositions of biological networks into monotone subsystems. In: Àlvarez, C., Serna, M. (eds.) WEA 2006. LNCS, vol. 4007, pp. 253–264. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  5. Feist, A.M., Scholten, J.C.M., Palsson, B.Ø., Brockman, F.J., Ideker, T.: Modeling methanogenesis with a genome scale metabolic reconstruction of Methanosarcina barkeri. Molecular Systems Biology, 2(2006.0004) (2006)Google Scholar
  6. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)Google Scholar
  7. Gabow, H.N.: Path-based depth-first search for strong and biconnected components. Information Processing Letters 74(3–4), 107–114 (2000)CrossRefMathSciNetGoogle Scholar
  8. Guo, J., Gramm, J., Hüffner, F., Niedermeier, R., Wernicke, S.: Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization. Journal of Computer and System Sciences 72(8), 1386–1396 (2006)MATHCrossRefMathSciNetGoogle Scholar
  9. Guo, J., Niedermeier, R.: Invitation to data reduction and problem kernelization. ACM SIGACT News (March 2007)Google Scholar
  10. Gutwenger, C., Mutzel, P.: A linear time implementation of SPQR-trees. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 77–90. Springer, Heidelberg (2001)Google Scholar
  11. Harary, F.: On the notion of balance of a signed graph. Michigan Mathematical Journal 2(2), 143–146 (1953)CrossRefMathSciNetGoogle Scholar
  12. Henzinger, M.R., Rao, S., Gabow, H.N.: Computing vertex connectivity: New bounds from old techniques. Journal of Algorithms 43(2), 222–250 (2000)CrossRefMathSciNetGoogle Scholar
  13. Hopcroft, J.E., Tarjan, R.E.: Dividing a graph into triconnected components. SIAM Journal on Computing 2(3), 135–158 (1973)CrossRefMathSciNetGoogle Scholar
  14. Hüffner, F.: Algorithm engineering for optimal graph bipartization. In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 240–252. Springer, Heidelberg (2005)Google Scholar
  15. Khot, S.: On the power of unique 2-prover 1-round games. In: Proc. 34th STOC, pp. 767–775. ACM Press, New York (2002)Google Scholar
  16. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)MATHGoogle Scholar
  17. Oda, K., Kimura, T., Matsuoka, Y., Funahashi, A., Muramatsu, M., Kitano, H.: Molecular interaction map of a macrophage. Research Report (August 2004), http://www.systems-biology.org/001/010.html
  18. Oda, K., Kitano, H.: A comprehensive, map of the toll-like receptor signaling network. Molecular Systems Biology, 2(2006.0015) (2006)Google Scholar
  19. Polzin, T., Vahdati Daneshmand, S.: Practical partitioning-based methods for the Steiner problem. In: Àlvarez, C., Serna, M. (eds.) WEA 2006. LNCS, vol. 4007, pp. 241–252. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2001)Google Scholar
  21. Volz, E.: Random networks with tunable degree distribution and clustering. Physical Review E, 70:056115 (2004)Google Scholar
  22. Zaslavsky, T.: Bibliography of signed and gain graphs. Electronic Journal of Combinatorics, DS8 (1998)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Falk Hüffner
    • 1
  • Nadja Betzler
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 JenaGermany

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