A new algorithm is put forward according to the characteristics of parallel calculation and local space-time of cellular automata model. In the algorithm, the critical path will develop with the evolvement of cells by selecting cells and setting corresponding rules. The experimental results indicate that this algorithm can be used to solve the critical path searching problem in multi-source-point and multi-collecting-point AOE network, eliminate the linear procedure of traditional algorithm based on topological sort and reverse topological scan, and also unify the algorithms of shortest path searching and critical path searching problems.

cellular automata; AOE network; critical path