The satisfiability threshold for randomly generated binary constraint satisfaction problems


  • This research was carried out during a visit to the Microsoft Research, Theory Group.

  • This research was carried out while the second author was a Visiting Researcher at Microsoft Research.


We study two natural models of randomly generated constraint satisfaction problems. We determine how quickly the domain size must grow with n to ensure that these models are robust in the sense that they exhibit a non-trivial threshold of satisfiability, and we determine the asymptotic order of that threshold. We also provide resolution complexity lower bounds for these models. One of our results immediately yields a theorem regarding homomorphisms between two random graphs. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006