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Give Me Another One!

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Algorithms and Computation (ISAAC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9472))

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Abstract

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.

Mike Behrisch and Gernot Salzer—Supported by Austrian Science Fund (FWF) grant I836-N23.

Miki Hermann—Supported by ANR-11-ISO2-003-01 Blanc International grant ALCOCLAN.

Stefan Mengel—Supported by QUALCOMM grant administered by École Polytechnique.

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Author information

Authors and Affiliations

  1. Technische Universität Wien, Vienna, Austria

    Mike Behrisch & Gernot Salzer

  2. LIX (UMR CNRS 7161), École Polytechnique, Palaiseau, France

    Miki Hermann & Stefan Mengel

Authors
  1. Mike Behrisch
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  2. Miki Hermann
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  3. Stefan Mengel
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  4. Gernot Salzer
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Corresponding author

Correspondence to Miki Hermann .

Editor information

Editors and Affiliations

  1. Masdar Institute, Abu Dhabi, United Arab Emirates

    Khaled Elbassioni

  2. Kyoto University, Kyoto, Japan

    Kazuhisa Makino

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Behrisch, M., Hermann, M., Mengel, S., Salzer, G. (2015). Give Me Another One!. In: Elbassioni, K., Makino, K. (eds) Algorithms and Computation. ISAAC 2015. Lecture Notes in Computer Science(), vol 9472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48971-0_56

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  • DOI: https://doi.org/10.1007/978-3-662-48971-0_56

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48970-3

  • Online ISBN: 978-3-662-48971-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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