带收入、预算和跳数约束的Steiner树问题的一个新的非线性规划
A new Integer Linear Program for the Steiner Tree Problem with Revenues, Budget and Hop Constraints
摘要：
带收入、预算和跳数约束的Steiner树问题（STPRBH）是经典Steiner树问题的一个变种。该问题要求给定图中的子树具有与其节点对应的最大收益，其中其总边成本遵守给定预算，并且每个节点与其根之间的边数不超过跳数限制。我们引入了一个新的二进制线性规划的多项式大小的偏序的基础上，（据我们所知）第一次解决了所有STPRBH实例从DIMACS基准集的最优性。该集合包含多达500个节点和12500条边的图形。
英文摘要：
The Steiner tree problem with revenues, budgets and hop constraints (STPRBH) is a variant of the classical Steiner tree problem. This problem asks for a subtree in a given graph with maximum revenues corresponding to its nodes, where its total edge costs respect the given budget, and the number of edges between each node and its root does not exceed the hop limit. We introduce a new binary linear program with polynomial size based on partial-ordering, which (up to our knowledge) for the first time solves all STPRBH instances from the DIMACS benchmark set to optimality. The set contains graphs with up to 500 nodes and 12500 edges.
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