Relay node placement, which aims to connect pre-deployed sensor nodes to base stations, is essential in minimizing the costs of wireless sensor networks. In this paper, we formulate the new Node-Weighted Partial Terminal Steiner Tree Problem (NWPTSTP) for minimum-cost relay node placement in two-tiered wireless sensor networks. The objective is to minimize the sum of heterogeneous production and placement costs of relay nodes and the sum of outage probabilities of transmission routes in a routing tree simultaneously. This extends the previous work that considers the costs of relay nodes to be homogeneous. After formulating NWPTSTP for this purpose, we prove that it can be transformed to the existing node-weighted Steiner tree problem. Subsequently, we conduct some theoretical analyses on the emerging Physarum-inspired algorithms to reveal their potential of computing Steiner trees. Based on these analyses, we propose a new Physarum-inspired algorithm for solving NWPTSTP. We conduct computational trials to show that: 1) in comparison to a state-of-the-art approximation algorithm for solving the node-weighted Steiner tree problem, our Physarum-inspired algorithm can produce better solutions in a smaller amount of time; and 2) in comparison to two state-of-the-art relay node placement algorithms, our Physarum-inspired algorithm can design wireless sensor networks with 25% lower relay cost and similar quality of service (specifically, 5% shorter network lifetime, 2% longer delay, and 0% loss of goodput). This indicates the usefulness of our Physarum-inspired algorithm for minimum-cost relay node placement in budget-limited scenarios.

中文翻译：

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一种基于物理灵感的无线传感器网络中成本最低的中继节点放置算法

中继节点的放置旨在将预先部署的传感器节点连接到基站，这对于最小化无线传感器网络的成本至关重要。在本文中，我们为两层无线传感器网络中的最小成本中继节点制定了新的节点加权部分终端斯坦纳树问题（NWPTSTP）。目的是使中继节点的异构生产和放置成本的总和与同时在路由树中的传输路径的中断概率的总和最小。这扩展了先前的工作，后者认为中继节点的成本是同质的。为此制定了NWPTSTP之后，我们证明可以将其转换为现有的节点加权Steiner树问题。后来，我们对受Physarum启发的新兴算法进行了一些理论分析，以揭示它们在计算Steiner树上的潜力。基于这些分析，我们提出了一种新的基于Physarum的算法来解决NWPTSTP。我们进行的计算试验表明：1）与解决节点加权Steiner树问题的最新近似算法相比，我们受Physarum启发的算法可以在更短的时间内产生更好的解决方案；和2）与两种最先进的中继节点放置算法相比，我们受Physarum启发的算法可以设计无线传感器网络，其中继成本降低25％，服务质量相近（具体而言，网络寿命缩短5％，2 ％的延迟时间，以及0％的吞吐量损失）。