Two Algorithms for Unranking Arborescences

Colbourn, Day, and Nel developed the first algorithm requiring at mostO(n3) arithmetic operations for ranking and unranking spanning trees of a graph (nis 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 requiresO(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.

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