Random subcubes as a toy model for constraint satisfaction problems

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. Keywords Constraint satisfaction problems · Clustering of solutions · Exactly solvable models

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Thierry Mora, Lenka Zdeborová
• Keywords: Constraint Satisfaction, CORR 2007, Education, Exactly Solvable, Solvable Random-subcube Model