Complements and transitive closures

Executable Transitive Closures

We provide a generic work-list algorithm to compute the (reflexive-)transitive closure of relations where only successors of newly detected states are generated. In contrast to our previous work [2], the relations do not have to be finite, but each element must only have finitely many (indirect) successors. Moreover, a subsumption relation can be used instead of pure equality. An executable var...

Transitive Dependencies in Transaction Closures

Complex applications consist of a large set of transactions which are interrelated. There are different kinds of dependencies among transactions of a complex application, e.g. termination or execution dependencies which are constraints on the occurrence of significant transaction events. In this paper, we analyze a set of (orthogonal) transaction dependencies. Here, we do not follow traditional...

Maintenance of Transitive Closures and Transitive Reductions of Graphs

General Transitive Closures and Aggregate Functions

General transitive closures are a convenient operation for process ing recursive structures with relational languages because they are easy to understand e ciently 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 closur...

Estimating the Size of Generalized Transitive Closures

We present a framework for the estimation of the size of binary recursively defined relations. We show how the framework can be used to provide estimating algo rithms for the size of the transitive closure and generalizations of the transitive closure, and also show that for bounded degree relations, the algorithm runs in linear time. Such estimating algorithms are essential if database systems...