An algebraic formulation of the aggregative closure query

AbstractThe aggregative closure problem, a transitive closure problem with aggregations on transitive paths, is formally defined by database terms. Its definition in our paper holds only on the subset conditions of path algebra, thereby it is more general than other definitions in previous works. For the completion of the definition, we suggest conditions for the existence of the fixpoint and classified the conditions as the properties of the aggregate operators and the problem domain. So we can verify the existence of the fixpoint by the suggested conditions. The naive algorithm is proposed as a computational semantics for the aggregative closure problem. This study also proves that for an aggregative closure problem the semi-naive algorithm is computationally equivalent to the naive algorithm when the aggregate product operator is distributive over aggregate sum operator

General Transitive Closures and Aggregate Functions

General transitive closures are a convenient operation for processing recursive structures with relational languages, because they are easy to understand, efficiently to implement and expressive enough to support a broad range of practical applications. To further extend the expressiveness of general transitive closures, we study the use of aggregate functions together with general transitive closures. While general transitive closures are restricted to express linear recursion, general transitive closures with aggregate functions can be used to express some nonlinear recursions too. We will give some conditions for general transitive closures with aggregate functions to be well formed and bottom up evalueable. We show how these constructs can be integrated in an extended SQL. Keywords: deductive databases, recursive query processing, SQL, general transitive closure

General Transitive Closures and Aggregate Functions

General transitive closures are a convenient operation for processing recursive structures with relational languages, because they are easy to understand, efficiently to implement and expressive enough to support a broad range of practical applications. To further extend the expressiveness of general transitive closures, we study the use of aggregate functions together with general transitive closures. While general transitive closures are restricted to express linear recursion, general transitive closures with aggregate functions can be used to express some nonlinear recursions too. We will give some conditions for general transitive closures with aggregate functions to be well formed and bottom up evalueable. We show how these constructs can be integrated in an extended SQL