Abstract: Structural testing is an effective way to test either procedural programs or object-oriented programs, and the branch coverage criterion has been proved to be the best cost-effective one of its all criteria. Through deeply investigating the properties of DD-graph and analyzing the shortcomings of the algorithm FTPS, an approximate algorithm (called Find_SemiUE) for solving the set of unconstrained arcs is presented, which is simple, quick and very suitable for the large-scale programs. Based on the forward (backward) breadth (depth) spanning trees, a simplified algorithm (called Generate_PathSet) for generating path cases which are executed in branch testing, is also proposed. This algorithm gains a dramatic improvement not only in time complexity but also in space complexity. Furthermore, the obtained conclusions are helpful for further research about DD-graph.