Advanced Coarsening Schemes for Graph Partitioning
- 13 Citations
- 1.2k Downloads
Abstract
The graph partitioning problem is widely used and studied in many practical and theoretical applications. Today multilevel strategies represent one of the most effective and efficient generic frameworks for solving this problem on large-scale graphs. Most of the attention in designing multilevel partitioning frameworks has been on the refinement phase. In this work we focus on the coarsening phase, which is responsible for creating structurally similar to the original but smaller graphs. We compare different matching- and AMG-based coarsening schemes, experiment with the algebraic distance between nodes, and demonstrate computational results on several classes of graphs that emphasize the running time and quality advantages of different coarsenings.
Keywords
Coarse Level Graph Partitioning Fast Version Multilevel Algorithm Graph Partitioning ProblemPreview
Unable to display preview. Download preview PDF.
References
- 1.Safro, I., Sanders, P., Schulz, C.: Advanced coarsening schemes for graph partitioning. Technical Report ANL/MCS-P2016-0112, Argonne National Laboratory (2012)Google Scholar
- 2.Bui, T.N., Jones, C.: Finding good approximate vertex and edge partitions is NP-hard. Inf. Process. Lett. 42(3), 153–159 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
- 3.Pothen, A., Simon, H.D., Liou, K.P.: Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11(3), 430–452 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
- 4.Fiduccia, C.M., Mattheyses, R.M.: A Linear-Time Heuristic for Improving Network Partitions. In: 19th Conference on Design Automation, pp. 175–181 (1982)Google Scholar
- 5.Sanders, P., Schulz, C.: Distributed Evolutionary Graph Partitioning. In: 12th Workshop on Algorithm Engineering and Experimentation (2011)Google Scholar
- 6.Schloegel, K., Karypis, G., Kumar, V.: Graph partitioning for high performance scientific simulations. In: Dongarra, J., et al. (eds.) CRPC Par. Comp. Handbook. Morgan Kaufmann (2000)Google Scholar
- 7.Pellegrini, F.: Scotch home page, http://www.labri.fr/pelegrin/scotch
- 8.Ron, D., Safro, I., Brandt, A.: Relaxation-based coarsening and multiscale graph organization. Multiscale Modeling & Simulation 9(1), 407–423 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
- 9.Sanders, P., Schulz, C.: Engineering Multilevel Graph Partitioning Algorithms. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 469–480. Springer, Heidelberg (2011)CrossRefGoogle Scholar
- 10.Chevalier, C., Safro, I.: Comparison of Coarsening Schemes for Multilevel Graph Partitioning. In: Stützle, T. (ed.) LION 3. LNCS, vol. 5851, pp. 191–205. Springer, Heidelberg (2009)CrossRefGoogle Scholar
- 11.Walshaw, C.: Multilevel refinement for combinatorial optimisation problems. Annals of Operations Research 131(1), 325–372 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
- 12.Holtgrewe, M., Sanders, P., Schulz, C.: Engineering a Scalable High Quality Graph Partitioner. In: 24th IEEE International Parallal and Distributed Processing Symposium (2010)Google Scholar
- 13.Chen, J., Safro, I.: Algebraic distance on graphs. SIAM Journal on Scientific Computing 33(6), 3468–3490 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
- 14.Brandt, A.: Multiscale scientific computation: Review 2001. In: Barth, T., Haimes, R., Chan, T. (eds.) Proceeding of the Yosemite Educational Symposium on Multiscale and Multiresolution Methods. Springer (October 2000)Google Scholar
- 15.Maue, J., Sanders, P.: Engineering Algorithms for Approximate Weighted Matching. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 242–255. Springer, Heidelberg (2007)CrossRefGoogle Scholar
- 16.Safro, I., Sanders, P., Schulz, C.: Benchmark with Potentially Hard Graphs for Partitioning Problem, http://www.mcs.anl.gov/~safro/hardpart.html
- 17.Bader, D., Meyerhenke, H., Sanders, P., Wagner, D.: 10th DIMACS Implementation Challenge - Graph Partitioning and Graph Clustering, http://www.cc.gatech.edu/dimacs10/
- 18.Lescovec, J.: Stanford Network Analysis Package (SNAP), http://snap.stanford.edu/index.html
- 19.Safro, I., Ron, D., Brandt, A.: Multilevel algorithms for linear ordering problems. Journal of Experimental Algorithmics 13, 1.4–1.20 (2008)Google Scholar