Constraint Satisfaction Problems Parameterized above or below Tight Bounds: A Survey

  • Gregory Gutin
  • Anders Yeo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7370)


We consider constraint satisfaction problems parameterized above or below tight bounds. One example is MaxSat parameterized above m/2: given a CNF formula F with m clauses, decide whether there is a truth assignment that satisfies at least m/2 + k clauses, where k is the parameter. Among other problems we deal with are MaxLin2-AA (given a system of linear equations over \(\mathbb{F}_2\) in which each equation has a positive integral weight, decide whether there is an assignment to the variables that satisfies equations of total weight at least W/2 + k, where W is the total weight of all equations), Max-r-Lin2-AA (the same as MaxLin2-AA, but each equation has at most r variables, where r is a constant) and Max-r-Sat-AA (given a CNF formula F with m clauses in which each clause has at most r literals, decide whether there is a truth assignment satisfying at least \(\sum_{i=1}^m(1-2^{r_i})+k\) clauses, where k is the parameter, r i is the number of literals in Clause i, and r is a constant). We also consider Max-r-CSP-AA, a natural generalization of both Max-r-Lin2-AA and Max-r-Sat-AA, order (or, permutation) constraint satisfaction problems of arities 2 and 3 parameterized above the average value and some other problems related to MaxSat. We discuss results, both polynomial kernels and parameterized algorithms, obtained for the problems mainly in the last few years as well as some open questions.


Boolean Function Constraint Satisfaction Problem Vertex Cover Truth Assignment Reduction Rule 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gregory Gutin
    • 1
  • Anders Yeo
    • 2
  1. 1.Royal Holloway, University of LondonEghamUK
  2. 2.University of JohannesburgAuckland ParkSouth Africa

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