This study builds up two parallel algorithms to improve computing performance for two listing binary and listing permutation algorithms. The problems are extremely interesting and practically applicable in many fields in our daily life. To parallel execution, we divide the data set input and allocate them to the processors. The article focuses on (i) the analysis of the research situation of the related works to compare and evaluate the existing problems of previous works, (ii) the analysis of the input data structure to divide data for the sub processors, (iii) the construction of parallel algorithms - proof of correctness and analysis of computing complexity, and (iv) experiments in multi-processing MPI and Thread library. Then the comparison of the results of the parallel algorithm with the sequential algorithm and the comparison of the execution time on different sub processors is discussed.