A performance study of transitive closure algorithms

Abstract

We present a comprehensive performance evaluation of transitive closure (reachability) algorithms for databases. The study is based upon careful implementations of the algorithms, measures page I/O, and covers algorithms for full transitive closure as well as partial transitive closure (finding all successors of each node in a set of given source nodes). We examine a wide range of acyclic graphs with varying density and “locality” of arcs in the graph. We also consider query parameters such as the selectivity of the query, and system parameters such as the buffer size and the page and successor list replacement policies. We show that significant cost tradeoffs exist between the algorithms in this spectrum and identify the factors that influence the performance of the algorithms. An important aspect of our work is that we measure a number of different cost metrics, giving us a good understanding of the predictive power of these metrics with respect to I/O cost. This is especially significant since metrics such as number of tuples generated or number of successor list operations have been widely used to compare transitive closure algorithms in the literature. Our results strongly suggest that these other metrics cannot be reliability used to predict I/O cost of transitive closure evaluation.