Parallel Computing Laboratory, Chengdu University of Information Technology, Chengdu, China; University of Electronic Science & Technology of China, Chengdu, China

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Abstract—The concepts of algorithm dynamics are proposed. Simulated annealing algorithm is analyzed by algorithm dynamics method. In the optimization progress metropolis criteria acts as an important role to construct simulated annealing algorithm. The metropolis criteria leads algorithm system to the ground state. At high temperature metropolis criteria make the algorithm system move like free particles, in this stage classic thermodynamics is suitable to analyze the algorithm. At low temperature metropolis criteria restricts the algorithm system vibration in the local area like crystal lattice vibration, in this stage quantum theory is suitable to analyze the algorithm. According to quantum dynamics the solution’s distribution of algorithm is Gaussian function. This results can interpret the implicit parallelism of algorithm. Uncertainty principle of algorithm (UPA) is proposed based on algorithm dynamics too. It indicates that precision and implicit parallelism of algorithm can’t achieve at the same time. Finally computational complexity is analyzed by thermodynamics. This method can get the lower bound of the algorithm easily. The computational complexity of sort problem’s lower bound is analyzed by thermodynamics method. The computational complexity is decided only by initial state and final state of the problems. The algorithm’s details are needless in this method.

Index Terms—algorithm dynamics, simulated annealing algorithm, implicit parallelism, quantum mechanics, thermodynamics, uncertainty principle of algorithm

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Cite: Peng Wang, " Algorithm Dynamics Analysis Method," Journal of Computers vol. 5, no. 2, pp. 178-185, 2010.