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Erschienen in:
2016 | OriginalPaper | Buchkapitel
As Close as It Gets
verfasst von : Mike Behrisch, Miki Hermann, Stefan Mengel, Gernot Salzer
Erschienen in: WALCOM: Algorithms and Computation
Verlag: Springer International Publishing
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Abstract
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.