Given a connected graph $G$ and a terminal set $R \subseteq V(G)$, the Steiner tree problem (ST) asks for a tree that spans all of $R$ with at most $r$ vertices from $V(G)\backslash R$, for some integer $r\geq 0$. It is known from (Garey et al.,1977 ) that ST is NP-complete. A Steiner tree in which all terminal vertices are constrained to be leaves is called a terminal Steiner tree. Our study addresses the existence of a terminal Steiner tree, its complexity across various graph classes, black-box applications of the ST, and a fixed-parameter tractable (FPT) algorithm with respect to the number of terminals.

翻译：给定一个连通图$G$和一个终端集$R \subseteq V(G)$，Steiner树问题（ST）要求找到一棵树，该树覆盖$R$中所有顶点，且包含至多$r$个来自$V(G)\backslash R$的顶点，其中$r \geq 0$为整数。已知（Garey等，1977）ST是NP完全的。若一棵Steiner树中所有终端顶点均为叶节点，则称其为终端Steiner树。本研究探讨终端Steiner树的存在性、其在各类图上的复杂性、ST的黑箱应用，以及一个关于终端数量的固定参数易处理（FPT）算法。