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

TL;DR

This paper investigates the computational complexity of clearing directed subgraphs with mobile agents, focusing on various problem variants, and provides results on their tractability, hardness, and parameterized complexity.

Contribution

It introduces new problem variants related to clearing directed subgraphs and analyzes their computational complexity and tractability.

Findings

Identifies polynomial-time solvable cases.

Establishes NP-hardness for certain variants.

Provides parameterized complexity results.

Abstract

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 on the variant, their initial positions may be pre-specified. In general, for a given 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) the underlying graph of $H$ includes a Steiner tree for $\mathcal{S}$ in $D$. We provide several results on the polynomial time tractability, hardness, and parameterized complexity of the problem.