
doi: 10.1002/nla.2326
AbstractThe goal of the present paper is the design of embeddings of a general sparse graph into a set of points in for appropriated ≥ 2. The embeddings that we are looking at aim to keep vertices that are grouped in communities together and keep the rest apart. To achieve this property, we utilize coarsening that respects possible community structures of the given graph. We employ a hierarchical multilevel coarsening approach that identifies communities (strongly connected groups of vertices) at every level. The multilevel strategy allows any given (presumably expensive) graph embedding algorithm to be made into a more scalable (and faster) algorithm. We demonstrate the presented approach on a number of given embedding algorithms and large‐scale graphs and achieve speed‐up over the methods in a recent paper.
Statistics and Probability, Iterative numerical methods for linear systems, Multigrid methods; domain decomposition for boundary value problems involving PDEs, Parallel numerical computation, multilevel algorithms, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, embeddings, Mathematics, sparse graphs, Numerical methods for ill-posed problems for boundary value problems involving PDEs
Statistics and Probability, Iterative numerical methods for linear systems, Multigrid methods; domain decomposition for boundary value problems involving PDEs, Parallel numerical computation, multilevel algorithms, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, embeddings, Mathematics, sparse graphs, Numerical methods for ill-posed problems for boundary value problems involving PDEs
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