Preprocessing of Min Ones Problems: A Dichotomy

  • Stefan Kratsch
  • Magnus Wahlström
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6198)


Min Ones Constraint Satisfaction Problems, i.e., the task of finding a satisfying assignment with at most k true variables (Min Ones SAT(Γ)), can express a number of interesting and natural problems. We study the preprocessing properties of this class of problems with respect to k, using the notion of kernelization to capture the viability of preprocessing. We give a dichotomy of Min Ones SAT(Γ) problems into admitting or not admitting a kernelization with size guarantee polynomial in k, based on the constraint language Γ. We introduce a property of boolean relations called mergeability that can be easily checked for any Γ. When all relations in Γ are mergeable, then we show a polynomial kernelization for Min Ones SAT(Γ). Otherwise, any Γ containing a non-mergeable relation and such that Min Ones SAT(Γ) is NP-complete permits us to prove that Min Ones SAT(Γ) does not admit a polynomial kernelization unless NP ⊆ co-NP/poly, by a reduction from a particular parameterization of Exact Hitting Set.


Constraint Satisfaction Problem Polynomial Kernel True Variable Satisfying Assignment Constraint Language 
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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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Stefan Kratsch
    • 1
  • Magnus Wahlström
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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