In this work, we suggest concepts and solution methodologies for a series of strategic network design problems that find application in highly data-sensitive industries, such as, for instance, the high-tech, governmental, or military sector. Our focus is on the installation of widely used cost-efficient tree-structured communication infrastructure. As base model we use the well-known Steiner tree problem, in which we are given terminal nodes, optional Steiner nodes, and potential network links between nodes. Its objective is to connect all terminals to a distributor node using a tree of minimum total edge costs. The novel, practically relevant side constraints are related to privacy concerns of customers, represented by terminals. In order to account for these, we study four privacy models that restrict the eligible infrastructure for the customer-distributor data exchange: (I) Selected pairs of terminals mutually exclude themselves as intermediate data-transmission nodes; (II) some pairs of terminals require disjoint paths to the distributor; (III) individual terminals forbid routing their data through allegedly untrustworthy links; and (IV) certain terminals do not allow the usage of doubtful links on their entire network branch. These topological data-privacy requirements significantly complicate the notoriously hard optimization problem. We clarify the model relationships by establishing dominance results, point out potential extensions and derive reduction tests. We present corresponding, strong non-compact integer programming (IP) formulations and embed these in efficient cutting plane methods. In addition, we develop constraint programming formulations that are used complementally to derive primal solutions. In a computational study, we analyze the performance of our methods on a diverse set of literature-based test instances.

在这项工作中，我们为一系列战略性网络设计问题提出了概念和解决方法，这些问题可以在高度数据敏感的行业中找到应用，例如高科技，政府或军事部门。我们的重点是安装广泛使用的具有成本效益的树状通信基础架构。作为基本模型，我们使用众所周知的Steiner树问题，其中给我们提供了终端节点，可选的Steiner节点以及节点之间的潜在网络链接。其目标是使用最小的总边缘成本树将所有终端连接到分发器节点。新颖的，实际相关的侧面约束与终端所代表的客户的隐私问题有关。为了解决这些问题，我们研究了四个隐私模型，这些模型限制了符合条件的基础结构，以进行客户-分销商数据交换：（II）某些端子对需要与分配器不相交的路径；（III）各个终端禁止通过所谓的不可信链接路由其数据；（IV）某些终端不允许在其整个网络分支上使用可疑链路。这些拓扑数据保密性要求使众所周知的困难的优化问题变得非常复杂。我们通过建立优势结果来阐明模型之间的关系，指出潜在的扩展并进行归约测试。我们提出了相应的，强大的非紧凑整数编程（IP）公式，并将其嵌入有效的切割平面方法中。此外，我们开发了约束编程公式，这些公式可互补地用于得出原始解。在计算研究中，我们分析了在各种基于文献的测试实例上我们的方法的性能。