  An arborescence, which is a directed analogue of a spanning tree in an
undirected graph, is one of the most fundamental combinatorial objects in a
digraph. In this paper, we study arborescences in digraphs from the viewpoint
of combinatorial reconfiguration, which is the field where we study
reachability between two configurations of some combinatorial objects via some
specified operations. Especially, we consider reconfiguration problems for
time-respecting arborescences, which were introduced by Kempe, Kleinberg, and
Kumar. We first prove that if the roots of the initial and target
time-respecting arborescences are the same, then the target arborescence is
always reachable from the initial one and we can find a shortest
reconfiguration sequence in polynomial time. Furthermore, we show if the roots
are not the same, then the target arborescence may not be reachable from the
initial one. On the other hand, we show that we can determine whether the
target arborescence is reachable form the initial one in polynomial time.
Finally, we prove that it is NP-hard to find a shortest reconfiguration
sequence in the case where the roots are not the same. Our results show an
interesting contrast to the previous results for (ordinary) arborescences
reconfiguration problems.
