Finding Good Approximate Vertex and Edge Partitions is NP-Hard

By T. N. Bui, Curt Jones. 1992

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Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering (2016, background): “And the last step is the graph pooling operation that trades spatial resolution for higher filter resolution.”
Localized matrix factorization for recommendation based on matrix block diagonal forms (2013, methodology): “Graph partitioning is known to be NP-hard [7], but this problem has been investigated extensively, and many efficient and highquality heuristic-based methods have been proposed [15], such as multilevel methods [14, 6], spectral partitioning [3] and kernel-based methods [2].”
Advanced Coarsening Schemes for Graph Partitioning (2012, background): “This problem is NP-complete even for several restricted classes of graphs, and there is no constant factor approximation algorithm for general graphs [6].”
Improve collaborative filtering through bordered block diagonal form matrices (2013, background): “Unfortunately, the minimum vertex cut problem is known to be NP-hard [5], but this problem has been investigated extensively, and many eﬃ-cient and high-quality heuristic-based methods have been proposed [15], such as the multilevel approach, spectral partitioning and kernel-based methods.”
Improved approximation algorithms for minimum-weight vertex separators (2005, methodology): “This in turn can be used to obtain polynomial-time approximation schemes for several problems in such graphs.”