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Channel routing is a key problem in the area of VLSI layout. Finding a minimum width solution of channel routing was proved to be NP-hard by Szymanski. In this paper, we come to a conclusion that the minimum parallel clique cover of $CCG$ is equivalent to the optimal solution of 2-layer manhattan channel routing where vertical constrains are noncyclic and extra empty columns and doglegs are not allowed. We also gave a new heuristic algorithm based on the conclusion to solve the problem of 2-layer manhattan channel routing.