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Random Subcubes as a Toy Model for Constraint Satisfaction Problems

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Abstract

We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring problems, and undergoes the same phase transitions as these problems. The comparison becomes quantitative in the large-k limit. Distance properties, as well the x-satisfiability threshold, are studied. The model is also generalized to define a continuous energy landscape useful for studying several aspects of glassy dynamics.

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Authors and Affiliations

  1. Lewis Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, 08544, USA

    Thierry Mora

  2. Université Paris-Sud, LPTMS, UMR8626, Bât. 100, Université Paris-Sud, 91405, Orsay cedex, France

    Lenka Zdeborová

  3. CNRS, LPTMS, UMR8626, Bât. 100, Université Paris-Sud, 91405, Orsay cedex, France

    Lenka Zdeborová

Authors
  1. Thierry Mora
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  2. Lenka Zdeborová
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Correspondence to Thierry Mora.

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Mora, T., Zdeborová, L. Random Subcubes as a Toy Model for Constraint Satisfaction Problems. J Stat Phys 131, 1121–1138 (2008). https://doi.org/10.1007/s10955-008-9543-x

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  • DOI: https://doi.org/10.1007/s10955-008-9543-x

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