Delaying Satisfiability for Random 2SAT

: Let (C1, C1), (C2, C2), . . . , (Cm, Cm) be a sequence of ordered pairs of 2CNF clauses chosen uniformly at random (with repetition) from the set of all 4 n 2 clauses on n variables. Choosing exactly one clause from each pair defines a probability distribution over 2CNF formulas. The choice at each step must be made on-line, without backtracking, but may depend on the clauses chosen previously. We show that there exists an on-line choice algorithm in the above process which results whp in a satisfiable 2CNF formula as long as m/n (1000/999)1/4. This contrasts with the well-known fact that a random m-clause formula constructed without the choice

• Type: Conference
• Year: 2010
• Where: APPROX
• Authors: Alistair Sinclair, Dan Vilenchik
• Keywords: Algorithms, APPROX 2010, On-line Choice Algorithm, Probability Distribution, Satisfiable 2CNF Formula