  Motivated by an application in network security, we investigate the following
"linear" case of Directed Mutlicut. Let $G$ be a directed graph which includes
some distinguished vertices $t_1, \ldots, t_k$. What is the size of the
smallest edge cut which eliminates all paths from $t_i$ to $t_j$ for all $i <
j$? We show that this problem is fixed-parameter tractable when parametrized in
the cutset size $p$ via an algorithm running in $O(4^p p n^4)$ time.
