Phase transition in a random NK landscape model Original Research Article

An analysis for the phase transition in a random NK landscape model, image, is given. This model is motivated from population genetics and the solubility problem for the model is equivalent to a random image-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 image with image is asymptotically insoluble. Based on empirical results, they conjectured that the phase transition occurs around the value image. We prove that an instance generated by image with image is soluble with positive probability by providing a polynomial time algorithm. Using branching process arguments, we prove again that an instance generated by image with image is asymptotically insoluble. The results show the phase transition around image for image. 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.