Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Kernelization, MaxLin Above Average

  • Anders Yeo
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_532

Years and Authors of Summarized Original Work

  • 2010; Crowston, Gutin, Jones, Kim, Ruzsa

  • 2011; Gutin, Kim, Szeider, Yeo

  • 2014; Crowston, Fellows, Gutin, Jones, Kim, Rosamond, Ruzsa, Thomassé, Yeo

Problem Definition

The problem MaxLin2 can be stated as follows. We are given a system of m equations in variables x1, , xn where each equation is \(\prod _{i\in I_{j}}x_{i} = b_{j}\)


Fixed-parameter tractability above lower bounds Kernelization Linear equations M-sum-free sets 
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Crowston R, Fellows M, Gutin G, Jones M, Kim EJ, Rosamond F, Ruzsa IZ, Thomassé S, Yeo A (2014) Satisfying more than half of a system of linear equations over GF(2): a multivariate approach. J Comput Syst Sci 80(4):687–696MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Crowston R, Gutin G, Jones M (2010) Note on Max Lin-2 above average. Inform Proc Lett 110:451–454MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Crowston R, Gutin G, Jones M, Kim EJ, Ruzsa I (2010) Systems of linear equations over \(\mathbb{F}_{2}\) and problems parameterized above average. In: SWAT 2010, Bergen. Lecture notes in computer science, vol 6139, pp 164–175Google Scholar
  4. 4.
    Downey RG, Fellows MR (2013) Fundamentals of parameterized complexity. Springer, London/Heidelberg/New YorkzbMATHCrossRefGoogle Scholar
  5. 5.
    Flum J, Grohe M (2006) Parameterized complexity theory. Springer, BerlinzbMATHGoogle Scholar
  6. 6.
    Gutin G, Kim EJ, Szeider S, Yeo A (2011) A probabilistic approach to problems parameterized above or below tight bounds. J Comput Syst Sci 77:422–429MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Gutin G, Yeo A (2012) Constraint satisfaction problems parameterized above or below tight bounds: a survey. Lect Notes Comput Sci 7370:257–286zbMATHCrossRefGoogle Scholar
  8. 8.
    Håstad J (2001) Some optimal inapproximability results. J ACM 48:798–859MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Håstad J, Venkatesh S (2004) On the advantage over a random assignment. Random Struct Algorithms 25(2):117–149MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Kim EJ, Williams R (2012) Improved parameterized algorithms for above average constraint satisfaction. In: IPEC 2011, Saarbrücken. Lecture notes in computer science, vol 7112, pp 118–131Google Scholar
  11. 11.
    Mahajan M, Raman V (1999) Parameterizing above guaranteed values: MaxSat and MaxCut. J Algorithms 31(2):335–354. Preliminary version in Electr. Colloq. Comput. Complex. (ECCC), TR-97-033, 1997Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Anders Yeo
    • 1
    • 2
  1. 1.Engineering Systems and DesignSingapore University of Technology and DesignSingaporeSingapore
  2. 2.Department of MathematicsUniversity of JohannesburgAuckland ParkSouth Africa