Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph
  Laplacians   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 multigrid method in the geometric setting
for elliptic eigenvalue problems and show its uniform convergence under certain
assumptions. Numerical tests are presented for computing the Fiedler vector of
several practical graphs, and numerical results show the efficiency and
optimality of our proposed cascadic multigrid algorithm.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas