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We study several problems of clearing subgraphs by mobile agents in digraphs.The agents can move only along directed walks of a digraph and, depending onthe variant, their initial positions may be pre-specified. In general, for agiven subset~$\mathcal{S}$ of vertices of a digraph $D$ and a positive integer$k$, the objective is to determine whether there is a subgraph$H=(\mathcal{V}_H,\mathcal{A}_H)$ of $D$ such that (a) $\mathcal{S} \subseteq\mathcal{V}_H$, (b) $H$ is the union of $k$ directed walks in $D$, and (c) theunderlying graph of $H$ includes a Steiner tree for $\mathcal{S}$ in $D$. Weprovide several results on the polynomial time tractability, hardness, andparameterized complexity of the problem.

The Snow Team Problem (Clearing Directed Subgraphs by Mobile Agents)