Adaptive aggregation on graphs
Provides theoretical error estimators for graph aggregation, but the impact is incremental as it extends existing finite element techniques to graphs without clear practical advantages.
The paper generalizes a posteriori error estimates from finite elements to graphs, using them to construct adaptive aggregation-based coarse spaces for graph Laplacians. Numerical examples demonstrate the effectiveness of the reshaping algorithm.
We generalize some of the functional (hyper-circle) a posteriori estimates from finite element settings to general graphs or Hilbert space settings. We provide several theoretical results in regard to the generalized a posteriori error estimators. We use these estimates to construct aggregation based coarse spaces for graph Laplacians. The estimator is used to assess the quality of an aggregation adaptively. Furthermore, a reshaping algorithm based is tested on several numerical examples.