Let $G = (V, E)$ be an undirected graph and let $B \subseteq V \times V$ be a set of terminal pairs. A node/edge multicut is a subset of vertices/edges of $G$ whose removal destroys all the paths between every terminal pair in $B$. The problem of computing a {\em minimum} node/edge multicut is NP-hard and extensively studied from several viewpoints. In this paper, we study the problem of enumerating all {\em minimal} node multicuts. We give an incremental polynomial delay enumeration algorithm for minimal node multicuts, which extends an enumeration algorithm due to Khachiyan et al. (Algorithmica, 2008) for minimal edge multicuts. Important special cases of node/edge multicuts are node/edge {\em multiway cuts}, where the set of terminal pairs contains every pair of vertices in some subset $T \subseteq V$, that is, $B = T \times T$. We improve the running time bound for this special case: We devise a polynomial delay and exponential space enumeration algorithm for minimal node multiway cuts and a polynomial delay and space enumeration algorithm for minimal edge multiway cuts.

中文翻译：

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最小多路切割和多路切割的高效枚举

令 $G = (V, E)$ 是一个无向图，让 $B \subseteq V \times V$ 是一组终端对。节点/边多重切割是 $G$ 的顶点/边的子集，其删除会破坏 $B$ 中每个终端对之间的所有路径。计算 {\em minimum} 节点/边多重切割的问题是 NP-hard 问题，并且从多个角度进行了广泛研究。在本文中，我们研究了枚举所有 {\em minimum} 节点多重切割的问题。我们给出了最小节点多切割的增量多项式延迟枚举算法，它扩展了由于 Khachiyan 等人的枚举算法。(Algorithmica, 2008) 用于最小边缘多切割。节点/边多重切割的重要特例是节点/边 {\em 多重切割}，其中终端对集包含某个子集 $T \subseteq V$ 中的每对顶点，即 $B = T \times T $.