Give Me Another One!

  • Mike Behrisch
  • Miki HermannEmail author
  • Stefan Mengel
  • Gernot Salzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9472)


We investigate the complexity of an optimization problem in Boolean propositional logic related to information theory: Given a conjunctive formula over a set of relations, find a satisfying assignment with minimal Hamming distance to a given assignment that satisfies the formula (\(\mathsf {NearestOtherSolution}\), \(\mathsf {NOSol}\)).

We present a complete classification with respect to the relations admitted in the formula. We give polynomial-time algorithms for several classes of constraint languages. For all other cases we prove hardness or completeness regarding \(\mathrm {poly{\text {-}}APX}\), \(\mathrm {NPO}\), or equivalence to a well-known hard optimization problem.


Minimum Hamming Distance Give Polynomial Time Algorithms Dual Horn Boolean Relation Atomic Constraints 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Mike Behrisch
    • 1
  • Miki Hermann
    • 2
    Email author
  • Stefan Mengel
    • 2
  • Gernot Salzer
    • 1
  1. 1.Technische Universität WienViennaAustria
  2. 2.LIX (UMR CNRS 7161)École PolytechniquePalaiseauFrance

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