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.
Partially supported by DFG SA 933/10-1 and CSCAPES institute, a DOE project.
This paper is a short version of the technical report [1]
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Safro, I., Sanders, P., Schulz, C.: Advanced coarsening schemes for graph partitioning. Technical Report ANL/MCS-P2016-0112, Argonne National Laboratory (2012)
Bui, T.N., Jones, C.: Finding good approximate vertex and edge partitions is NP-hard. Inf. Process. Lett. 42(3), 153–159 (1992)
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)
Fiduccia, C.M., Mattheyses, R.M.: A Linear-Time Heuristic for Improving Network Partitions. In: 19th Conference on Design Automation, pp. 175–181 (1982)
Sanders, P., Schulz, C.: Distributed Evolutionary Graph Partitioning. In: 12th Workshop on Algorithm Engineering and Experimentation (2011)
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)
Pellegrini, F.: Scotch home page, http://www.labri.fr/pelegrin/scotch
Ron, D., Safro, I., Brandt, A.: Relaxation-based coarsening and multiscale graph organization. Multiscale Modeling & Simulation 9(1), 407–423 (2011)
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)
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)
Walshaw, C.: Multilevel refinement for combinatorial optimisation problems. Annals of Operations Research 131(1), 325–372 (2004)
Holtgrewe, M., Sanders, P., Schulz, C.: Engineering a Scalable High Quality Graph Partitioner. In: 24th IEEE International Parallal and Distributed Processing Symposium (2010)
Chen, J., Safro, I.: Algebraic distance on graphs. SIAM Journal on Scientific Computing 33(6), 3468–3490 (2011)
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)
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)
Safro, I., Sanders, P., Schulz, C.: Benchmark with Potentially Hard Graphs for Partitioning Problem, http://www.mcs.anl.gov/~safro/hardpart.html
Bader, D., Meyerhenke, H., Sanders, P., Wagner, D.: 10th DIMACS Implementation Challenge - Graph Partitioning and Graph Clustering, http://www.cc.gatech.edu/dimacs10/
Lescovec, J.: Stanford Network Analysis Package (SNAP), http://snap.stanford.edu/index.html
Safro, I., Ron, D., Brandt, A.: Multilevel algorithms for linear ordering problems. Journal of Experimental Algorithmics 13, 1.4–1.20 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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. https://doi.org/10.1007/978-3-642-30850-5_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-30850-5_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30849-9
Online ISBN: 978-3-642-30850-5
eBook Packages: Computer ScienceComputer Science (R0)