The Satisfiability Threshold for a Seemingly Intractable Random Constraint Satisfaction Problem

We determine the exact threshold of satisfiability for random instancesof a particular NP-complete constraint satisfaction problem (CSP). This isthe first random CSP model for which we have determined a precise linearsatisfiability threshold, and for which random instances with density nearthat threshold appear to be computationally difficult. More formally,it is the first random CSP model for which the satisfiability thresholdis known and which shares the following characteristics with random k-SAT for k ≥ 3. The problem is NP-complete, the satisfiability thresholdoccurs when there is a linear number of clauses, and a uniformly randominstance with a linear number of clauses asymptotically almost surely hasexponential resolution complexity.