Graph Decomposition and Transitive Closures

Abstract. In this paper, we propose a new algorithm for computing recursive closures. The main idea behind this is tree labeling and graph decomposition, based on which the transitive closure of a directed graph can be computed in O(e⋅b) time and O(n⋅b) space, where n is the number of the nodes of the graph, e is the numbers of the edges, and b is the graph’s breadth. It is a better computational complexity than any existing algorithms for this problem. 1