SUDA2 is a recursive search algorithm for minimal unique itemset detection. Such sets of items are formed via combinations of non-obvious attributes enabling individual record identification. The nature of SUDA2 allows work to be divided into non-overlapping tasks enabling parallel execution. Earlier work developed a parallel implementation for SUDA2 on an SMP cluster, and this was found to be several orders of magnitude faster than sequential SUDA2. However, if fixed-granularity parallel tasks are scheduled naively in the order of their generation, the system load tends to be imbalanced with little work at the beginning and end of the search. This paper investigates the effectiveness of variable-grained and dynamic work generation strategies for parallel SUDA2. These methods restrict the number of sub-tasks to be generated, based on the criterion of probable work size. The further we descend in the search recursion tree, the smaller the tasks become, thus we only select the largest tasks at each level of recursion as being suitable for scheduling. The revised algorithm runs approximately twice as fast as the existing parallel SUDA2 for finer levels of granularity when variable-grained work generation is applied. The dynamic method, performing level-wise task selection based on size, outperforms the other techniques investigated.

A new algorithm, SUDA2, is presented which finds minimally unique itemsets i.e., minimal itemsets of frequency one. These itemsets, referred to as Minimal Sample Uniques (MSUs), are important for statistical agencies who wish to estimate the risk of disclosure of their datasets. SUDA2 is a recursive algorithm which uses new observations about the properties of MSUs to prune and traverse the search space. Experimental comparisons with previous work demonstrate that SUDA2 is several orders of magnitude faster, enabling datasets of significantly more columns to be addressed. The ability of SUDA2 to identify the boundaries of the search space for MSUs is clearly demonstrated.

A new algorithm for minimal infrequent itemset mining is presented. Potential applications of finding infrequent itemsets include statistical disclosure risk assessment, bioinformatics, and fraud detection. This is the first algorithm designed specifically for finding these rare itemsets. Many itemset properties used implicitly in the algorithm are proved. The problem is shown to be NP-complete. Experimental results are then presented.

We perform a statistical analysis and describe the asymptotic behavior of the frequency and size distribution of δoccurrent, minimal δ-occurrent, and maximal δ-occurrent itemsets occurring in random datasets across the entire spectrum of δ. We also describe the probability distribution of the support of an n-element itemset in a random dataset. We find that for small values of δ relative to number of transactions the size distribution of δ-occurrent itemsets and maximal δ-occurrent itemsets can be approximated by the binomial distributions b(L, 1 1+2δ ) and b(L, 1 2δ ), respectively, where L is inventory size. The ratio of minimal δ-occurrent and maximal δ-occurrent itemsets to the total number of δ-occurrent itemsets is low for small values of δ and rapidly approaches 1 as δ approaches the number of transactions. We also prove that the probability distribution of the support of an n-element itemset in a random k-transaction dataset is binomial of type b(k, 1 2n ).

Ten or more forward speeds and two or more reverse speed are achieved by a planetary gear train of an automatic transmission that includes three planetary gear sets mounted on an input shaft, an output shaft disposed in parallel with the input shaft and having an output gear. The transmission further includes six shafts respectively interconnecting corresponding elements among the input shaft and rotational elements of the three planetary gear sets, a first transfer gear selectively delivering torque between one of the six shafts and the output shaft; and a second transfer gear selectively delivering torque between the output shaft and one rotational element of the third planetary gear set.

The importance of being able to classify records according to disclosure risk is well understood; Skinner and Holmes (1998), Fienberg and Makov (1998). One concept for so classifying records is called special uniqueness; see Elliot (2000), Elliot et al (2002), Manning and Haglin (2005). This paper describes SUDA (Special Uniques Detection Algorithm) which is both a set of computer science algorithms and indeed a fully functioning software system for detecting and grading special uniques. Section 1 describes the basic design principles behind the sequential SUDA algorithm. Section 2 describes the software (now in use at the UK Office for National Statistics and Australian Bureau of Statistics). Section 3 describes recent advances (i) in parallelising SUDA and improving the algorithm so that cross-classifications of up to 60 variables can be comprehensively analysed (ii) in developing a version of SUDA for Grid computing.

Association rule discovery techniques have gradually been adapt-ed to parallel systems in order to take advantage of the higher speed and greater storage capacity that they offer. The transition to a distributed memory system requires the partitioning of the database among the processors, a procedure that is generally carried out indiscriminately. However, for some techniques the nature of the database partitioning can have a pronounced impact on execution time and attention will be focused on one such algorithm, Fast Parallel Mining (FPM). A new algorithm, Data Allocation Algorithm (DAA), is presented that uses Principal Component Analysis to improve the data distribution prior to FPM.