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.
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics