Abstract We are given a graph G = ( V ∪ T , E ) , with V ∪ T the set of vertices where T is a set of terminals and E the set of edges. The multi-terminal vertex separator problem consists in finding a subset of vertices S ⊆ V of minimum size intersecting all paths between every pair of terminals. In this paper we present three extended linear integer programming formulations for the multi-terminal vertex separator problem and we develop Branch-and-Price and Branch-and-Cut-and-Price algorithms. For each formulation we present the pricing problem, the branching scheme and the computation of the dual bound used during the column generation phase. Computational results are reported comparing the performance of the formulations on a set of instances.

中文翻译：

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多终端顶点分隔符问题：Branch-and-Cut-and-Price

摘要 我们给出了一个图 G = ( V ∪ T , E ) ，其中 V ∪ T 是顶点的集合，其中 T 是一组终端，而 E 是边的集合。多终端顶点分离器问题在于找到与每对终端之间的所有路径相交的最小尺寸的顶点 S ⊆ V 的子集。在本文中，我们针对多终端顶点分隔符问题提出了三个扩展的线性整数规划公式，并开发了 Branch-and-Price 和 Branch-and-Cut-Price 算法。对于每个公式，我们都提出了定价问题、分支方案和列生成阶段使用的双界计算。计算结果报告了在一组实例上比较配方的性能。