In a cardinality constrained inverse center location problem on networks, the goal is to modify the edge lengths at the minimum total cost subject to the given modification bounds so that a prespecified vertex becomes an absolute center location of the underlying network under the perturbed edge lengths and further the cardinality of the modified edge lengths obeys an upper bound. Using a set of self-constructed red-black search trees, as a suitable data structure, we propose novel optimal algorithms with polynomial time complexities for the problem on tree networks under various cost norms.

中文翻译：

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具有边长增加的树网络上的基数约束逆中心定位问题

在网络上的基数约束逆中心位置问题中，目标是在给定的修改范围内，以最小的总成本修改边长，以使预先指定的顶点成为受扰动边长和以下边长的基础网络的绝对中心位置。此外，修改后的边长的基数服从上限。使用一组自构造的红黑搜索树作为合适的数据结构，针对各种成本准则下的树型网络问题，我们提出了具有多项式时间复杂度的新颖最优算法。