Advanced Coarsening Schemes for Graph Partitioning

Ilya Safro; Peter Sanders; Christian Schulz

doi:10.1007/978-3-642-30850-5_32

International Symposium on Experimental Algorithms

SEA 2012: Experimental Algorithms pp 369-380

Advanced Coarsening Schemes for Graph Partitioning

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Authors and affiliations

Ilya Safro
Peter Sanders
Christian Schulz

Conference paper

DOI: 10.1007/978-3-642-30850-5_32

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7276)

Cite this paper as:: Safro I., Sanders P., Schulz C. (2012) Advanced Coarsening Schemes for Graph Partitioning. In: Klasing R. (eds) Experimental Algorithms. SEA 2012. Lecture Notes in Computer Science, vol 7276. Springer, Berlin, Heidelberg

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.

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References

1.
Safro, I., Sanders, P., Schulz, C.: Advanced coarsening schemes for graph partitioning. Technical Report ANL/MCS-P2016-0112, Argonne National Laboratory (2012)
2.
Bui, T.N., Jones, C.: Finding good approximate vertex and edge partitions is NP-hard. Inf. Process. Lett. 42(3), 153–159 (1992)MathSciNetMATHCrossRefGoogle 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)MathSciNetMATHCrossRefGoogle 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)
5.
Sanders, P., Schulz, C.: Distributed Evolutionary Graph Partitioning. In: 12th Workshop on Algorithm Engineering and Experimentation (2011)
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)
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)MathSciNetMATHCrossRefGoogle 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)MathSciNetMATHCrossRefGoogle 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)
13.
Chen, J., Safro, I.: Algebraic distance on graphs. SIAM Journal on Scientific Computing 33(6), 3468–3490 (2011)MathSciNetMATHCrossRefGoogle 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)
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)

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Authors and Affiliations

Ilya Safro
- 1
Peter Sanders
- 2
Christian Schulz
- 2

1.Mathematics and Computer Science DivisionArgonne National LaboratoryUSA
2.Institute for Theoretical Informatics, Algorithmics IIKarlsruhe Institute of TechnologyGermany

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Advanced Coarsening Schemes for Graph Partitioning

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