As Close as It Gets

  • Mike Behrisch
  • Miki Hermann
  • Stefan Mengel
  • Gernot Salzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9627)


We study the minimum Hamming distance between distinct satisfying assignments of a conjunctive input formula over a given set of Boolean relations (\(\mathsf {MinSolutionDistance}\), \(\mathsf {MSD}\)). We present a complete classification of the complexity of this optimization problem 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 with respect to \(\text {poly-APX}\), or \(\mathrm {NPO}\), or equivalence to a well-known hard optimization problem.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

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

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