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. © 2008 Springer Science+Business Media, LLC.
CITATION STYLE
Mora, T., & Zdeborová, L. (2008). Random subcubes as a toy model for constraint satisfaction problems. Journal of Statistical Physics, 131(6), 1121–1138. https://doi.org/10.1007/s10955-008-9543-x
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