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We show an improved parallel algorithm for decomposing an undirected unweighted graph into small diameter pieces with a small fraction of the edges in between.
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Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs
P. Christiano, J. A. Kelner, A. Ma̧dry, D. Spielman, and S.-H. Teng · 2011
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Separator theorems for minor-free and shallow minor-free graphs with applications
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Using petal-decompositions to build a low stretch spanning tree
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Direction-optimizing breadth-first search
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G. E. Blelloch, A. Gupta, and K. Tangwongsan · 2012
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Nearly-linear work parallel sdd solvers, low-diameter decomposition, and low-stretch subgraphs
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