A pre-order walk of bullet tree on slides is actually a natural choice, since speakers of presentations often follow such an order to develop their talks, i.e., they discuss a parent bullet first and then each of its children in sequence.
although some remedies may be taken (Zhu et al., 2010), sequentializing the hierarchies before alignment, in principle, enforces a full linearity/monotonicity between transcripts and slide trees, which violates some basic properties of the problem that we will discuss.