Phase transition in a random NK landscape model

An analysis for the phase transition in a random NK landscape model is given. For the fixed ratio model, NK(n, k, z), Gao and Culberson [17] showed that a random instance generated by NK(n, 2, z) with z > z0 = 27−7 √ 5 4 is asymptotically insoluble. Based on empirical results, they conjectured that the phase transition occurs around the value z = z0. We prove that an instance generated by NK(n, 2, z) with z < z0 is soluble with positive probability by providing a variant of the unit clause algorithm. Using branching process arguments, we also reprove that an instance generated by NK(n, 2, z) with z > z0 is asymptotically insoluble. The results show the phase transition around z = z0 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. Keywords NK landscape, phase transition, random k-SAT problem, unit clause algorithm, branching process

• Type: Conference
• Year: 2005
• Where: GECCO
• Authors: Sung-Soon Choi, Kyomin Jung, Jeong Han Kim
• Keywords: GECCO 2005, NK Landscape, Phase Transition, Unit Clause Algorithm