The Design and Performance Study of Binary Transitive Closure Algorithms

Transitive closure operation is one of the most useful new operations in deductive database systems. When it is added to conventional relational database systems, most practical problems with recursion can be coped with. Therefore, efficient processing of transitive closure is an important task in deductive database systems. Transitive closure operation can be divided into total closure and query closure operations. To implement the operations, we can have unary or binary algorithms. A lot of work has been done on the efficient derivation of total closures and unary query closures, but not much work has been done on binary query closures. A binary query closure algorithm derives the transitive closure relevant to a set of query constants, associated with pairs of the initial query constants and their driven elements. The binary query closure operation is more frequently used than the unary one. In this research, 6 algorithms are developed for binary query transitive closure processing, namely Binary Wavefront, Unary Wavefront with Frontier-Edges, Unary Wavefront with Implied-Edges-Closure, Unary Wavefront Preprocessing with TotalFrontier-Edges, level-relaxed Binary Wavefront, and level-relaxed Unary Wavefront Preprocessing with Total-Frontier-Edges. These algorithms are analyzed and their relative performances are compared on their VO behavior and other processing costs. More importantly, the analysis is done on different characteristics of data and on different buffer sizes. Our analysis and performance study show that reference locality and data clustering play an important role in the performance of the algorithms. The ordering of the set of relational operations is also important in determining the 110 performance of the algorithms. Our research also demonstrates that the rate at which the disk VO of an algorithm decreases with the increase in buffer size is affected by the Maximum Buffer Requirement of the algorithm. Among the algorithms without level relaxation, Binary Wavefront outperforms the others in a wide range of data sets when the buffer size is small. Unary Wavefront Preprocessing with Total-Frontier-Edges Algorithm performs better when the number of query constants is small and the buffer size is large. A base relation that requires a lot of iterative processing and generates a large volume of answers to the transitive query is best processed by Unary Wavefront with Implied-Edges-Closure Algorithm. The analysis of the YO behavior of Unary Wavefront with Frontier-Edges Algorithm helps to develop a better algorithm, like the Unary Wavefront Preprocessing with Total-Frontier-Edges Algorithm. The level relaxed versions of the algorithms are best for clustered data. Our research provides insight into binary query closure processing. We hope that this will, in turn, stimulate further research on the processing of more complex recursions.