Journal of Statistical Physics

, Volume 131, Issue 6, pp 1121–1138 | Cite as

Random Subcubes as a Toy Model for Constraint Satisfaction Problems

  • Thierry MoraEmail author
  • Lenka Zdeborová


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.


Constraint satisfaction problems Clustering of solutions Exactly solvable models 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Lewis Sigler Institute for Integrative GenomicsPrinceton UniversityPrincetonUSA
  2. 2.Université Paris-Sud, LPTMS, UMR8626, Bât. 100Université Paris-SudOrsay cedexFrance
  3. 3.CNRS, LPTMS, UMR8626, Bât. 100Université Paris-SudOrsay cedexFrance

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