Graph sampling theory extends the traditional sampling theory to graphs with topological structures. As a key part of the graph sampling theory, subset selection chooses nodes on graphs as samples to reconstruct the original signal. Due to the eigen-decomposition operation for Laplacian matrices of graphs, however, existing subset selection methods usually require high-complexity calculations. In this paper, with an aim of enhancing the computational efficiency of subset selection on graphs, we propose a novel objective function based on the optimal experimental design. Theoretical analysis shows that this function enjoys an $\alpha$-supermodular property with a provable lower bound on $\alpha$. The objective function, together with an approximate of the low-pass filter on graphs, suggests a fast subset selection method that does not require any eigen-decomposition operation. Experimental results show that the proposed method exhibits high computational efficiency, while having competitive results compared to the state-of-the-art ones, especially when the sampling rate is low.

翻译：图表抽样理论将传统的抽样理论扩展到具有地形结构的图表。作为图表抽样理论的关键部分,子集选择图表上的节点作为样本来重建原始信号。然而,由于对拉普拉西亚图矩阵的天分分分解操作,现有的子集选方法通常需要高复杂度计算。在本文中,为了提高图表子集选的计算效率,我们根据最佳实验设计提出了一个新的客观功能。理论分析表明,该功能拥有一个$alpha$-超模特性,其可调低的值为$\alpha$。客观函数加上图表上的低射过滤器的近似值,表明一种不需要任何海分分分分解操作的快速子选择方法。实验结果显示,拟议方法在与最新技术相比具有高计算效率的同时,具有竞争性的结果,特别是在取样率低的情况下。