A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians

@article{Urschel2014ACM,
  title={A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians},
  author={John C. Urschel and Xiaozhe Hu and Jinchao Xu and Ludmil T. Zikatanov},
  journal={arXiv: Numerical Analysis},
  year={2014}
}
In this paper, we develop a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalue. This vector has been found to have applications in fields such as graph partitioning and graph drawing. The algorithm is a purely algebraic approach based on a heavy edge coarsening scheme and pointwise smoothing for refinement. To gain theoretical insight, we also consider the related cascadic… 
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