Efficient data aggregation is crucial for mobile wireless sensor networks, as their resources are significantly constrained. Over recent years, the average consensus algorithm has found a wide application in this technology. In this paper, we present a weight matrix simplifying the average consensus algorithm over mobile wireless sensor networks, thereby prolonging the network lifetime as well as ensuring the proper operation of the algorithm. Our contribution results from the theorem stating how the Laplacian spectrum of an undirected simple finite graph changes in the case of adding an arbitrary edge into this graph. We identify that the mixing parameter of Best Constant weights of a complete finite graph with an arbitrary order ensures the convergence in time-varying topologies without any reconfiguration of the edge weights. The presented theorems and lemmas are verified over evolving graphs with various parameters, whereby it is demonstrated that our approach ensures the convergence of the average consensus algorithm over mobile wireless sensor networks in spite of no edge reconfiguration.

中文翻译：

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移动无线传感器网络上的平均共识：权重矩阵确保收敛而无需重新配置边缘权重。

高效的数据聚合对于移动无线传感器网络至关重要，因为它们的资源受到极大限制。近年来，平均共识算法已在该技术中得到广泛应用。在本文中，我们提出了一种权重矩阵，简化了移动无线传感器网络上的平均共识算法，从而延长了网络寿命，并确保了算法的正确运行。我们的贡献来自定理，该定理指出在向该图添加任意边的情况下，无向简单有限图的拉普拉斯谱如何变化。我们确定，具有任意阶数的完整有限图的最佳恒定权重的混合参数可确保时变拓扑的收敛，而无需重新配置边缘权重。