Clearing directed subgraphs by mobile agents

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 S of vertices of a digraph D and a positive integer k, the objective is to determine whether there is a subgraph H = (V H , A H ) of D such that (a) S ⊆ 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 S in D. We provide several results on the polynomial time tractability, hardness, and parameterized complexity of the problem.