The solution of membership problem is essential to design an available algorithm of scheme decomposition. Because of the partial order among temporal types in strong partial ordered temporal scheme, it is difficult to solve its membership problem. The concepts of mixed dependency base on given temporal type, mixed dependency base in strong partial ordered scheme, mixed set closure of partial temporal functional dependency and temporal multi-valued dependency and mixed closure of strong partial ordered scheme were given. The algorithms of dependency base of attribution and closure of attribution sets were also given. On this basis, the algorithm of membership problem of mixed dependency set in strong partial ordered scheme was put forward. The proof for its termination, correction and time complexity were presented. Application examples show that the research on related theory and algorithm solves determination of the membership problem in strong partial ordered mixed dependencies, and provides a theoretical basis for solving the strong partial order temporal scheme and the design of temporal database standardization.
When using the way of pattern growth to construct tree structure, the exiting algorithms for mining probabilistic frequent itemsets suffer many problems, such as generating large number of tree nodes, occupying large memory space and having low efficiency. In order to solve these problems, a Progressive Uncertain Frequent Pattern Growth algorithm named PUFP-Growth was proposed. By the way of reading data in the uncertain database tuple by tuple, the proposed algorithm constructed tree structure as compact as Frequent Pattern Tree (FP-Tree) and updated dynamic array of expected value whose header table saved the same itemsets. When all transactions were inserted into the Progressive Uncertain Frequent Pattern tree (PUFP-Tree), all the probabilistic frequent itemsets could be mined by traversing the dynamic array. The experimental results and theoretical analysis show that PUFP-Growth algorithm can find the probabilistic frequent itemsets effectively. Compared with the Uncertain Frequent pattern Growth (UF-Growth) algorithm and Compressed Uncertain Frequent-Pattern Mine (CUFP-Mine) algorithm, the proposed PUFP-Growth algorithm can improve mining efficiency of probabilistic frequent itemsets on uncertain dataset and reduce memory usage to a certain degree.