  In this paper, we investigate the computational complexity of subgraph
reconfiguration problems in directed graphs. More specifically, we focus on the
problem of reconfiguring arborescences in a digraph, where an arborescence is a
directed graph such that its underlying undirected graph forms a tree and all
vertices have in-degree at most 1. Given two arborescences in a digraph, the
goal of the problem is to determine whether there is a (reconfiguration)
sequence of arborescences between the given arborescences such that each
arborescence in the sequence can be obtained from the previous one by removing
an arc and then adding another arc. We show that this problem can be solved in
polynomial time, whereas the problem is PSPACE-complete when we restrict
arborescences in a reconfiguration sequence to directed paths or relax to
directed acyclic graphs. We also show that there is a polynomial-time algorithm
for finding a shortest reconfiguration sequence between two spanning
arborescences.
