On the Hardness of Losing Weight

  • Andrei Krokhin
  • Dániel Marx
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)


We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a better (lighter, i.e., having strictly less Hamming weight) solution within a given distance from the initial solution. We classify the complexity, both classical and parameterized, of such problems by a Schaefer-style dichotomy result, that is, with a restricted set of allowed types of constraints. Our results show that there is a considerable amount of such problems that are NP-hard, but fixed-parameter tractable when parameterized by the distance.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andrei Krokhin
    • 1
  • Dániel Marx
    • 2
  1. 1.Department of Computer ScienceDurham UniversityDurhamUK
  2. 2.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary

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