An algorithm for enumerating all directed spanning trees in a directed graph

A directed spanning tree in a directed graph G = (V, A) is a spanning tree such that no two arcs share their tails. In this paper, we propose an algorithm for listing all directed spanning trees of G. Its time and space complexities are O(\A\+ND(\V\, \A\)) and O(\A\+DS(\V\, \A\)), where D(\V\, \A\) and DS(\V\, \A\) are the time and space complexities of the data structure for updating the minimum spanning tree in an undirected graph with \V\ vertices and \A\ edges. Here N denotes the number of directed spanning trees in G.