Benchmarking two types of restricted transitive closure algorithms

The authors present and evaluate two algorithms-one linear and one logarithmic-for the computation of the restricted transitive closure of a binary database relation. The algorithms are implemented in a relational database management system (Ingres), and on equipment which is fairly common in today´s database application environments. The performance evaluation reveals three important points. First, unlike the case of the complete transitive closure computations where the linear (seminaive) method is outperformed by the logarithmic methods, in the computation of the restricted transitive closure the opposite is true. Second, contrary to the popular belief that the algorithms run faster if the size of the intermediate result relations is decreased by deleting excess data, the fastest algorithms are those which attempt to delete no data. Unless deletions can be handled efficiently, their potential benefits are overshadowed by the cost incurred to perform them. Third, the operations union and difference are established as being significantly more expensive than the join operation in these algorithms