I am working on a very large dataset of a single DAG whose vertices have a low branching factor. I need to generate all possible (simple) paths starting from the source and write them to a file.

My question is: what is computational complexity class of this problem?

If this problem is NP-Hard, is there any relatively space-efficient algorithm that can generate this exponential number of paths iteratively?

*Any references are extremely appreciated.*

Thanks in advance.