Parameterized Study of Steiner Tree on Unit Disk Graphs

We study the Steiner Tree problem on unit disk graphs. Given a n vertex graph G, subset $$R\subseteq V(G)$$ of t vertices and positive integer k, objective is to decide if there exists tree T in G that spans over all R uses at most k from $$V\setminus R$$ . The are referred as terminals $$V(G)\setminus vertices. First, we show NP-hard. Next, prove graphs can be solved $$n^{O(\sqrt{t+k})}$$ time. also parameterized by has an FPT algorithm with running time $$2^{O(k)}n^{O(1)}$$ In fact, algorithms designed for more general class graphs, called clique-grid Fomin (Discret. Comput. Geometry 62(4):879–911, 2019). mention algorithmic results made work bounded aspect ratio. Finally, W[1]-hard.