Following the recent advances in the Internet of Things (IoT), it is drawing lots of attention to design distributed algorithms for various network optimization problems under the SINR (Signal-to-Interference-and-Noise-Ratio) interference model, such as spanner construction. Since a spanner can maintain a linear number of links while still preserving efficient routes for any pair of nodes in wireless networks, it is important to design distributed algorithms for spanners. Given a constant as the required stretch factor, the problem of our concern is to design an efficient distributed algorithm to construct a -spanner of the communication graph under SINR such that the delay for the task completion is minimized, where the delay is the time interval between the time slot that the first node commences its operation to the time slot that all the nodes finish their task of constructing the -spanner. Our main contributions include four aspects. First, we propose a proximity range and proximity independent set (PISet) to increase the number of nodes transmitting successfully at the same time in order to reduce the delay. Second, we develop a distributed randomized algorithm SINR-Spanner to construct a required -spanner with high probability. Third, the approximation ratio of SINR-Spanner is proven to be a constant. Finally, extensive simulations are carried out to verify the effectiveness and efficiency of our proposed algorithm.

中文翻译：

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SINRI下的物联网构建跨度

继物联网（IoT）的最新进展之后，人们开始关注针对SINR（信噪比和噪声比）干扰模型下的各种网络优化问题设计分布式算法，例如扳手施工。由于扳手可以保持线性数量的链接，同时仍为无线网络中的任何一对节点保留有效的路由，因此为扳手设计分布式算法非常重要。给定一个常数作为要求拉伸因子，我们关注的问题是设计一个高效的分布式算法，以构造一个- SINR下扳手通信图表，使得该任务完成的延迟被最小化，其中，所述延迟是时间之间的时间间隔插槽的第一个节点开始其操作的时间段，所有的节点完成其建设的任务-扳手。我们的主要贡献包括四个方面。首先，我们提出一个接近范围和接近无关集（PISet），以增加同时成功传输的节点数量，以减少延迟。其次，我们开发了一种分布式随机算法SINR-Spanner来构建所需的-扳手的可能性很高。第三，SINR-Spanner的近似比率被证明是一个常数。最后，进行了广泛的仿真以验证我们提出的算法的有效性和效率。