Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
Upper bounds on the satisfiability threshold
Theoretical Computer Science - Phase transitions in combinatorial problems
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation
Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation
Threshold phenomena in random graph colouring and satisfiability
Threshold phenomena in random graph colouring and satisfiability
Evolutionary Computation
The Gn,mphase transition is not hard for the Hamiltonian cycle problem
Journal of Artificial Intelligence Research
The computational complexity of N-K fitness functions
IEEE Transactions on Evolutionary Computation
Phase transition in a random NK landscape model
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Space Complexity of Estimation of Distribution Algorithms
Evolutionary Computation
Resolution complexity of random constraint satisfaction problems: another half of the story
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Phase transition in a random NK landscape model
Artificial Intelligence
Analysis of estimation of distribution algorithms and genetic algorithms on NK landscapes
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
Resolution complexity of random constraint satisfaction problems: Another half of the story
Discrete Applied Mathematics
On the treewidth of NK landscapes
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
NK landscapes, problem difficulty, and hybrid evolutionary algorithms
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Network crossover performance on NK landscapes and deceptive problems
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Adaptation of a multiagent evolutionary algorithm to NK landscapes
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
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In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the uniform probability model, we prove that the phase transition is easy in the sense that there is a polynomial algorithm that can solve a random instance of the problem with the probability asymptotic to 1 as the problem size tends to infinity. For the fixed ratio model, we establish several upper bounds for the solubility threshold, and prove that random instances with parameters above these upper bounds can be solved polynomially. This, together with our empirical study for random instances generated below and in the phase transition region, suggests that the phase transition of the fixed ratio model is also easy.