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Fixed-Parameter Tractability of almost CSP Problem with Decisive Relations

  • Chihao Zhang
  • Hongyang Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7285)

Abstract

Let I be an instance of binary boolean CSP. Consider the problem of deciding whether one can remove at most k constraints of I such that the remaining constraints are satisfiable. We call it the Almost CSP problem. This problem is NP-complete and we study it from the point of view of parameterized complexity where k is the parameter. Two special cases have been studied: when the constraints are inequality relations (Guo et al., WADS 2005) and when the constraints are OR type relations (Razgon and O’Sullivan, ICALP 2008). Both cases are shown to be fixed-parameter tractable (FPT). In this paper, we define a class of decisive relations and show that when all the relations are in this class, the problem is also fixed-parameter tractable. Note that the inequality relation is decisive, thus our result generalizes the result of the parameterized edge-bipartization problem (Guo et al., WADS 2005). Moreover as a simple corollary, if the set of relations contains no OR type relations, then the problem remains fixed-parameter tractable. However, it is still open whether OR type relations and other relations can be combined together while the fixed-parameter tractability still holds.

Keywords

Constraint Satisfaction Problem Type Relation Inequality Relation Decisive Relation Constraint Satisfaction Problem Instance 
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. 1.
    Chen, J., Liu, Y., Lu, S.: An improved parameterized algorithm for the minimum node multiway cut problem. Algorithmica 55(1), 1–13 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Chen, J., Liu, Y., Lu, S., O’Sullivan, B., Razgon, I.: A fixed-parameter algorithm for the directed feedback vertex set problem. Journal of the ACM (JACM) 55(5), 21 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Demaine, E., Gutin, G., Marx, D., Stege, U.: Open problems from dagstuhl seminar 07281, available electronically, Technical report, http://drops.dagstuhl.de/opus/volltexte/2007/1254/pdf/07281
  4. 4.
    Downey, R.G., Fellows, M.R.: Parameterized complexity. Springer, New York (1999)CrossRefGoogle Scholar
  5. 5.
    Flum, J., Grohe, M.: Parameterized complexity theory. Springer-Verlag New York Inc. (2006)Google Scholar
  6. 6.
    Guo, J., Gramm, J., Huffner, 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)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Guo, J., Moser, H., Niedermeier, R.: Iterative compression for exactly solving np-hard minimization problems. Algorithmics of Large and Complex Networks, 65–80 (2009)Google Scholar
  8. 8.
    Khot, S., Raman, V.: Parameterized complexity of finding subgraphs with hereditary properties. Theoretical Computer Science 289(2), 997–1008 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Mahajan, M., Raman, V.: Parametrizing above guaranteed values: Maxsat and maxcut. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 4 (1997)Google Scholar
  10. 10.
    Marx, D.: Parameterized graph separation problems. Theoretical Computer Science 351(3), 394–406 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Marx, D.: Important separators and parameterized algorithms (February 2011), http://www.cs.bme.hu/~dmarx/papers/marx-mds-separators-slides.pdf
  12. 12.
    Niedermeier, R.: Invitation to fixed-parameter algorithms, vol. 31. Oxford University Press, USA (2006)zbMATHCrossRefGoogle Scholar
  13. 13.
    Razgon, I., O’Sullivan, B.: Almost 2-sat is fixed-parameter tractable. Journal of Computer and System Sciences 75(8), 435–450 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Reed, B., Smith, K., Vetta, A.: Finding odd cycle transversals. Operations Research Letters 32(4), 299–301 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Wernicke, S.: On the algorithmic tractability of single nucleotide polymorphism (SNP) analysis and related problems. PhD thesis (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Chihao Zhang
    • 1
  • Hongyang Zhang
    • 1
  1. 1.BASICS, Department of Computer ScienceShanghai Jiao Tong UniversityShanghaiChina

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