The probabilistic analysis of a greedy satisfiability algorithm
Random Structures & Algorithms
Coloring complete bipartite graphs from random lists
Random Structures & Algorithms
A Better Algorithm for Random k-SAT
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Hiding satisfying assignments: two are better than one
Journal of Artificial Intelligence Research
On random betweenness constraints
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Random 2-XORSAT at the satisfiability threshold
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
IEEE Transactions on Information Theory
On random betweenness constraints
Combinatorics, Probability and Computing
A Better Algorithm for Random $k$-SAT
SIAM Journal on Computing
The decimation process in random k-SAT
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Independent sets in random graphs from the weighted second moment method
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
The condensation transition in random hypergraph 2-coloring
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Limit theorems for random MAX-2-XORSAT
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
On belief propagation guided decimation for random k-SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Exact thresholds for DPLL on random XOR-SAT and NP-complete extensions of XOR-SAT
Theoretical Computer Science
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
Going after the k-SAT threshold
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Many NP-complete constraint satisfaction problems appear to undergo a “phase transition” from solubility to insolubility when the constraint density passes through a critical threshold. In all such cases it is easy to derive upper bounds on the location of the threshold by showing that above a certain density the first moment (expectation) of the number of solutions tends to zero. We show that in the case of certain symmetric constraints, considering the second moment of the number of solutions yields nearly matching lower bounds for the location of the threshold. Specifically, we prove that the threshold for both random hypergraph 2-colorability (Property B) and random Not-All-Equal $k$-SAT is $2^{k-1}\ln 2 -O(1)$. As a corollary, we establish that the threshold for random $k$-SAT is of order $\Theta(2^k)$, resolving a long-standing open problem.