Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
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
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
Random k-Sat: A Tight Threshold For Moderately Growing k
Combinatorica
Random $k$-SAT: Two Moments Suffice to Cross a Sharp Threshold
SIAM Journal on Computing
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
Message-passing and local heuristics as decimation strategies for satisfiability
Proceedings of the 2009 ACM symposium on Applied Computing
A constructive proof of the general lovász local lemma
Journal of the ACM (JACM)
Combinatorial approach to the interpolation method and scaling limits in sparse random graphs
Proceedings of the forty-second ACM symposium on Theory of computing
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
On belief propagation guided decimation for random k-SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Bounds on threshold of regular random k-SAT
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Catching the k-NAESAT threshold
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The freezing threshold for k-colourings of a random graph
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Exponential lower bounds for DPLL algorithms on satisfiable random 3-CNF formulas
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Unsatisfiability bounds for random CSPs from an energetic interpolation method
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Random k-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely for any k≥3. The best current results, based on the second moment method, yield upper and lower bounds that differ by an additive k ⋅ {ln2}/2, a term that is unbounded in k (Achlioptas, Peres: STOC 2003). The basic reason for this gap is the inherent asymmetry of the Boolean values 'true' and 'false' in contrast to the perfect symmetry, e.g., among the various colors in a graph coloring problem. Here we develop a new asymmetric second moment method that allows us to tackle this issue head on for the first time in the theory of random CSPs. This technique enables us to compute the k-SAT threshold up to an additive ln2-1/2+O(1/k) ~0.19. Independently of the rigorous work, physicists have developed a sophisticated but non-rigorous technique called the "cavity method" for the study of random CSPs (Mezard, Parisi, Zecchina: Science~2002). Our result matches the best bound that can be obtained from the so-called "replica symmetric" version of the cavity method, and indeed our proof directly harnesses parts of the physics calculations.