Let $G$ be a directed, acyclic graph of order $n$, such that:
- $G$ has exactly one source vertex $s$;
- $G$ has exactly two sink vertices $t_1, t_2$;
- The out-degree of any non-sink vertex in $G$ is exactly 2; and
- The longest path from $s$ to either of $t_1,t_2$ has length $k$.
What is the most efficient way of finding all unique paths from $s$ to $t_1$ (or $t_2$, doesn't really matter in this case) in $G$? What would the time complexity of this algorithm be? It is acceptable to use $k$ as a parameter if that would produce a better analysis.