Abstract: In processing a query including a selection criterion on one or more attributes of a relation, a prior statistic generated for a prior different selection criterion on the same one or more attributes of the relation, may be revalidated for use in processing the query, based upon a measure of the entropy of the one or more attributes of the relation. In this way, the re-validation of statistics may be performed more efficiently. Furthermore, attribute groups of a relation for which multi-dimensional indexes are to be formed, are identified by evaluating the correlation of attribute values within tuples of the relation and determining that the correlation of attribute values within tuples of the relation exceeds a threshold.

Abstract: An apparatus and method authenticate computed results in a public distributed computing environment without the need for fully recomputing the results. The work unit is operated on by client code that computes one or more partial results along with the completed result. When the results are returned to the server, the server may decide to have a trusted computer system process the same work unit to compute the partial result according to a defined acceptance policy. In addition, the work unit name, user identity and current date are encrypted using a time-sensitive key. Should the server detect a problem with the results (e.g., decrypted work unit name does not match, recomputed partial result does not match), the results may be rejected according to a defined rejection policy. In this manner, it becomes very difficult to fool a server into thinking a work unit has been processed when it has not.