A process for generating a vector for testing a digital circuit for a given fault first creates a composite circuit including a fault-present version of the circuit and a fault-free version. An implication graph is developed for the composite circuit and its energy function is derived as a combination of binary and ternary terms. All signal states that are consistent with the circuit function minimize the energy function to zero value. The transitive closure is computed for the binary terms, and redundancies, contradictions, fixations, identification and exclusions are identified. By iteration of implication graphs and transitive closures together with arbitrarily assigned signal values all ternary terms of the energy function are converted to binary terms, after which transitive closure recomputes a set of literals that can be used to generate the desired test vector by a standard branch and bound procedure.

An agent collecting management data from the resource operating in the managed network to form a management data set and identifies segregated regions of management data within the management data set. Each segregated region is a respective partial transitive closure of the collected management data taken over a graph representing the entire management data set. For each segregated region of management data, the agent partitions that segregated region of management data into a set of logical partitions and transfers each logical partition of the segregated region of management data to a network management application in the managed network for access by the network management application. A network management application receives the partitions and only needs to keep objects in memory related to partitions that are currently received and being processed thus saving memory and processing resources.

The semantic integration problem for merging multiple databases of very large size, the merge/purge problem, can be solved by multiple runs of the sorted neighborhood method or the clustering method with small windows followed by the computation of the transitive closure over the results of each run. The sorted neighborhood method works well under this scheme but is computationally expensive due to the sorting phase. An alternative method based on data clustering that reduces the complexity to linear time making multiple runs followed by transitive closure feasible and efficient. A method is provided for identifying duplicate records in a database, each record having at least one field and a plurality of keys, including the steps of sorting the records according to a criteria applied to a first key; comparing a number of consecutive sorted records to each other, wherein the number is less than a number of records in said database and identifying a first group of duplicate records; storing the identity of the first group; sorting the records according to a criteria applied to a second key; comparing a number of consecutive sorted records to each other, wherein the number is less than a number of records in said database and identifying a second group of duplicate records; storing the identity of the second group; and subjecting the union of the first and second groups to transitive closure.

In a data processing system for management of a relational data base stored among a plurality of disc storage units, a method and apparatus for horizontally partitioning a physical page on the basis of tuples includes a master processor, a master disc storage unit coupled to the master processor, a plurality of slave processors controlled by the master processor, and a plurality of slave disc storage units, one coupled to each of the slave processors. The master disc storage unit stores, in the form of a B-tree structure, a clustered index for either an attribute or a relation to be processed in the relational data base. The plurality of slave disc storage units store divisionally a relation in the data base which is partitioned on the basis of a page for a clustered index thereof in such a manner that the plurality of slave processors may execute, in parallel, a plurality of processings on a cluster of tuples, as defined in their range in connection with a given key value of the clustered index.

In CD-players with a memory (S) having A storage locations for the storing of the titles recorded on a CD-record, it can occur that the number of titles C recorded on the CD-record exceeds the number of storage locations A in the CD-player. In order to keep the access times for individual titles low, the memory (S) is partitioned into a first part (T1), having B storage positions, and a second part T2, having A-B storage positions. The titles 1 to B are stored in sequence in the B storage locations of the T1 portion of memory S. The remaining titles are distributed to the A-B storage locations of the part (T2) such that, no continuing sequence with the first B titles is formed. For example, the remaining C-B titles may be distributed evenly in the second part (T2) of memory S.