Advanced Coarsening Schemes for Graph Partitioning - Ilya ... - KIT

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Stationary iterative relaxation rewrite process as x (k+1) = H JORx (k) , where 11 Ilya Safro, Peter Sanders, Christian Schulz: Advanced Coarsening Schemes for Graph Partititoning H JOR = (1 − α) I + αD −1 W ⇒ basically the JOR method to solve Lx = 0 L = D − W graph laplacian, α relaxation paramter H JOR lazy random walk matrix Department of Informatics Institute for Theoretical Computer Science, Algorithmics II
Stationary iterative relaxation rewrite process as x (k+1) = H JORx (k) , where 11 Ilya Safro, Peter Sanders, Christian Schulz: Advanced Coarsening Schemes for Graph Partititoning H JOR = (1 − α) I + αD −1 W ⇒ basically the JOR method to solve Lx = 0 Definition Extended 2-normed algebraic distance between i and j after k iterations x (k+1) = Hx (k) on R random initializations if {i, j} ∈ E, otherwise ρ (k) ij ρ (k) R ij := ∑ |x r=1 (k,r) i = 0 − x (k,r) j | 2 1/2 Department of Informatics Institute for Theoretical Computer Science, Algorithmics II
Page 1 and 2: 1 Advanced Coarsening Schemes for G
Page 3 and 4: Motivation Social Networks SNWs are
Page 5 and 6: Motivation Social Networks Graph Pa
Page 7 and 8: Multi-Level Graph Partitioning Succ
Page 9 and 10: Algebraic Distance Relaxation Proce
Page 11 and 12: Algebraic Distance Example - random
Page 13: Stationary iterative relaxation rew
Page 17 and 18: Coarse Nodes C-points Selection fin
Page 19 and 20: Coarse Nodes classical AMG interpol
Page 21 and 22: Coarse Nodes modified AMG interpola
Page 23 and 24: Modified Algorithm Likelihood for v
Page 29 and 30: Experimental Results Social Network
Page 31 and 32: Experimental Results Potentially Ha
Page 33 and 34: Conclusion Experiments algebraic di

Advanced Coarsening Schemes for Graph Partitioning - Ilya ... - KIT

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