A general upper bound for the satisfiability threshold of random r-SAT formulae
Journal of Algorithms
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
Two-coloring random hypergraphs
Random Structures & Algorithms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Treshold for Unsatisfiability
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Random k-Sat: A Tight Threshold For Moderately Growing k
Combinatorica
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
Threshold values of random K-SAT from the cavity method
Random Structures & Algorithms
On the solution-space geometry of random constraint satisfaction problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Random $k$-SAT: Two Moments Suffice to Cross a Sharp Threshold
SIAM Journal on Computing
Reconstruction for Models on Random Graphs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Pairs of SAT-assignments in random Boolean formulæ
Theoretical Computer Science
Mick gets some (the odds are on his side) (satisfiability)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Algorithmic Barriers from Phase Transitions
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Analytic Combinatorics
A Better Algorithm for Random $k$-SAT
SIAM Journal on Computing
The condensation transition in random hypergraph 2-coloring
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A simple algorithm for random colouring G(n, d/n) using (2 + ε)d colours
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On independent sets in random graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Complete convergence of message passing algorithms for some satisfiability problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Going after the k-SAT threshold
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The best current estimates of the thresholds for the existence of solutions in random constraint satisfaction problems ('CSPs') mostly derive from the first and the second moment method. Yet apart from a very few exceptional cases these methods do not quite yield matching upper and lower bounds. According to deep but non-rigorous arguments from statistical mechanics, this discrepancy is due to a change in the geometry of the set of solutions called condensation that occurs shortly before the actual threshold for the existence of solutions (Krzakala, Montanari, Ricci-Tersenghi, Semerjian, Zdeborova: PNAS~2007). To cope with condensation, physicists have developed a sophisticated but non-rigorous formalism called Survey Propagation (Me-zard, Parisi, Zecchina: Science 2002). This formalism yields precise conjectures on the threshold values of many random CSPs. Here we develop a new Survey Propagation inspired second moment method for the random k-NAESAT problem, which is one of the standard benchmark problems in the theory of random CSPs. This new technique allows us to overcome the barrier posed by condensation rigorously. We prove that the threshold for the existence of solutions in random k-NAESAT is 2k-1ln2-(ln/2 2+1/4)+εk, where |εk| ≤ 2-(1-ok(1))k, thereby verifying the statistical mechanics conjecture for this problem.