A new approach is presented for organizing a large collection of multidimensional data with an unknown distribution by partitioning the data such that the data are relatively homogeneously distributed in each block. A multidimensional tree is generated according to this partition. After the tree is generated, summary data estimation such as selectively estimation can be performed via a tree search. This approach is applicable to both ordered and categorial attributes. The merits of this method are verified theoretically and by simulation.>

A data model and an access method for summary data management are proposed. Summary data, represented as a trinary tuple, consist of metaknowledge summarized by a statistical function of a category of individual information typically stored in a conventional database. The concept of category (type or class) and the additivity property of statistical functions form a basis for the model that allows for the derivation of summary data. The complexity of deriving summary data has been found computationally intractable in general, and the proposed summary data model, with disjointness constraint, solves the problem without the loss of information. The proposed access method, called the summary data tree, or SD-tree, which handles an orthogonal category as a hyperrectangle, realizes the proposed summary data model. The structure of the SD-tree provides for efficient operations including summary data search, derivation, and insertion on the stored summary data.>

A data model and an access method for summary data management are presented. Summary data, represented as a trinary tuple (statistical function, category, summary), are metaknowledge summarized by a statistical function of a category of individual information typically stored in a conventional database. For instance, (average-income, female engineer with 10 years' experience and master's degree, $45000) is a summary datum. The computational complexity of the derivability problem has been found intractable in general, and the proposed summary data model, enforcing the disjointness constraint, alleviates the intractable problem without loss of information. In order to store, manage, and access summary data, a multidimensional access method called summary data (SD) tree is proposed. By preserving the category hierarchy, the SD tree provides for efficient operations, including summary data search, derivation, insertion, and deletion.>

The notion of a qualified function is introduced as a general means of representing the parameters of dynamic systems. Two specific types of qualified functions are defined for the analysis of the behavior and performance of structured programs. Transformation functions represent the values of variables during execution and timing algorithms express the execution times of programs symbolically. Complete rules of derivation for transformation functions and timing algorithms are given for the control mechanisms of sequence, selection, fixed loop, and while statement. Deterministic and stochastic simplification of transformation functions and timing algorithms are investigated and methods of eliminating recursion for expressions corresponding to while statements are studied.