Abstract
We determine the complexity of an optimization problem related to information theory. Taking a conjunctive propositional formula over some finite set of Boolean relations as input, we seek a satisfying assignment of the formula having minimal Hamming distance to a given assignment that is not required to be a model (NearestSolution, NSol). We obtain a complete classification with respect to the relations admitted in the formula. For two classes of constraint languages we present polynomial time algorithms; otherwise, we prove hardness or completeness concerning the classes APX, poly-APX, NPO, or equivalence to well-known hard optimization problems.
The title refers to the Alabama Song by Bertolt Brecht (lyrics), Kurt Weill (music), and Elisabeth Hauptmann (English translation). Among the numerous cover versions, the one by Jim Morrison and the Doors became particularly popular in the 1970s.
M. Behrisch, and G. Salzer — Supported by Austrian Science Fund (FWF) grant I836-N23.
M. Hermann — Supported by ANR-11-ISO2-003-01 Blanc International grant ALCOCLAN.
S. Mengel — Research of this author was done during his post-doctoral stay in LIX at École Polytechnique. Supported by a QUALCOMM grant.
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Behrisch, M., Hermann, M., Mengel, S., Salzer, G. (2016). The Next Whisky Bar. In: Kulikov, A., Woeginger, G. (eds) Computer Science – Theory and Applications. CSR 2016. Lecture Notes in Computer Science(), vol 9691. Springer, Cham. https://doi.org/10.1007/978-3-319-34171-2_4
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DOI: https://doi.org/10.1007/978-3-319-34171-2_4
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