A New Algorithm for Transitive Closures and Computation of Recursion in relational Databases

In this paper, we propose a new algorithm for computing recursive closures. The main idea behind this algorithm is tree labeling and graph decomposition, based on which the transitive closure of a directed graph can be computed in O(e⋅dmax⋅dout) time and in O(n⋅dmax⋅dout) space, where n is the number of the nodes of the graph, e is the numbers of the edges, dmax is the maximal indegree of the nodes, and dout is the average outdegree of the nodes. Especially, this method can be used to efficiently compute recursive relationships of a directed graph in a relational environment.