Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
Information Sciences: an International Journal
A threshold for unsatisfiability
Journal of Computer and System Sciences
Adaptation on rugged landscapes
Management Science
Setting 2 variables at a time yields a new lower bound for random 3-SAT (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Bounding the unsatisfiability threshold of random 3-SAT
Random Structures & Algorithms
The scaling window of the 2-SAT transition
Random Structures & Algorithms
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
Fitness landscapes and evolvability
Evolutionary Computation
Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms
Proceedings of the 6th International Conference on Genetic Algorithms
Optimal myopic algorithms for random 3-SAT
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Maximally rugged NK landscapes contain the highest peaks
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Global optima results for the Kauffman NK model
Mathematical Programming: Series A and B
Evolutionary Computation
An analysis of phase transition in NK landscapes
Journal of Artificial Intelligence Research
New entropy-based measures of gene significance and epistasis
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
On the treewidth of NK landscapes
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
The computational complexity of N-K fitness functions
IEEE Transactions on Evolutionary Computation
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An analysis for the phase transition in a random NK landscape model, NK(n,k,z), is given. This model is motivated from population genetics and the solubility problem for the model is equivalent to a random (k+1)-SAT problem. Gao and Culberson [Y. Gao, J. Culberson, An analysis of phase transition in NK landscapes, Journal of Artificial Intelligence Research 17 (2002) 309-332] showed that a random instance generated by NK(n,2,z) with zz"0=27-754 is asymptotically insoluble. Based on empirical results, they conjectured that the phase transition occurs around the value z=z"0. We prove that an instance generated by NK(n,2,z) with zz"0 is asymptotically insoluble. The results show the phase transition around z=z"0 for NK(n,2,z). In the course of the analysis, we introduce a generalized random 2-SAT formula, which is of self interest, and show its phase transition phenomenon.