In big data environment, the mass of nodes in graph and the complexity of analysis bring forward higher requirement for the speed and accuracy of maximum clique problems. In order to solve the problems, a Parallel Multi-layer Graph Partitioning method for Solving Maximum Clique (PMGP_SMC) was proposed. Firstly, a new Multi-layer Graph Partitioning method (MGP) was proposed, the large-scale graph partitioning was executed to generate subgraphs while the clique structure of the original graph was maintained and not destroyed. Large-scale subgraphs were divided into multi-level graphs to further reduce the size of subgraphs. The graph computing framework of GraphX was used to achieve MGP to form a Parallel Multi-layer Graph Partitioning (PMGP) method. Then, according to the size of partitioned subgraph, the iteration number of Local Search algorithm Based on Penalty value (PBLS) was reduced, and the PBLS based on Speed optimization (SPBLS) was proposed to solve the maximum clique of each subgraph. Finally, PMGP method and SPBLS were combined to form PMGP_SMC. The large-scale dataset of Stanford was used for running test. The experimental results show that, the proposed PMGP reduces the maximum subgraph size by more than 100 times and the average subgraph size by 2 times compared with Parallel Single Graph Partitioning method (PSGP). Compared with PSGP for Solving Maximum Clique (PSGP_SMC), the proposed PMGP_SMC reduces the overall time by about 100 times, and its accuracy is consistent with that of Parallel Multi-layer Graph Partitioning for solving maximum clique based on Maximal Clique Enumeration (PMGP_MCE) in solving the maximum clique. The proposed PMGP_SMC can solve the maximum clique of large-scale graph quickly and accurately.

In order to further improve the execution efficiency of Frequent Pattern-Growth (FP-Growth) algorithm on Spark platform, a new parallel FP-Growth algorithm based on Spark, named BFPG (Better Frequent Pattern-Growth), was presented. Firstly, the grouping strategy F-List was improved in the size of the Frequent Pattern-Tree (FP-Tree) and the amount of partition calculation to ensure that the load sum of each partition was approximately equal. Secondly, the data set partitioning strategy was optimized by creating a list P-List, and then the time complexity was reduced by reducing the traversal times. The experimental results show that the BFPG algorithm improves the mining efficiency of the parallel FP-Growth algorithm, and the algorithm has good scalability.