Two Algorithms for Unranking Arborescences

Colbourn, Day, and Nel developed the first algorithm requiring at most O(n³) arithmetic operations for ranking and unranking spanning trees of a graph (n is the number of vertices of the graph). We present two algorithms for the more general problem of ranking and unranking rooted spanning arborescences of a directed graph. The first is conceptually very simple and requires O(n³) arithmetic operations. The second approach shows that the number of arithmetic operations can be reduced to the same as that of the best known algorithms for matrix multiplication.