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Advanced coarsening schemes for graph partitioning. (English) Zbl 1347.68355


MSC:

68W05 Nonnumerical algorithms
05C12 Distance in graphs
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C82 Small world graphs, complex networks (graph-theoretic aspects)
68W40 Analysis of algorithms

References:

[1] D. A. Bader, H. Meyerhenke, P. Sanders, and D. Wagner. 2013. 10th DIMACS Implementation Challenge—Graph Partitioning and Graph Clustering. Retrieved October 20, 2014, from http://www.cc.gatech.edu/dimacs10/. · Zbl 1262.05001
[2] G. Bartel, C. Gutwenger, K. Klein, and P. Mutzel. 2010. An experimental evaluation of multilevel layout methods. In Graph Drawing. Lecture Notes in Computer Science, Vol. 6502. Springer, 80-91. · Zbl 1314.68217
[3] A. Brandt. 2001. Multiscale scientific computation: Review 2001. In Multiscale and Multiresolution Methods. Lecture Notes in Computational Science and Engineering, Vol. 20. Springer, 3-95. · Zbl 0989.65140
[4] A. Brandt and D. Ron. 2003. Multigrid solvers and multilevel optimization strategies. In Multilevel Optimization in VLSICAD. Combinatorial Optimization, Vol. 14. Springer, 1-69. · Zbl 1046.65043
[5] T. N. Bui and C. Jones. 1992. Finding good approximate vertex and edge partitions is NP-hard. Information Processing Letters 42, 3, 153-159. · Zbl 0764.68061
[6] T. N. Bui and B. R. Moon. 1996. Genetic algorithm and graph partitioning. IEEE Transactions on Computers 45, 7, 841-855. DOI: http://dx.doi.org/10.1109/12.508322 · Zbl 1049.68605
[7] J. Chen and I. Safro. 2011. Algebraic distance on graphs. SIAM Journal on Scientific Computing 33, 6, 3468-3490. · Zbl 1235.05042
[8] C. Chevalier and I. Safro. 2009. Comparison of coarsening schemes for multilevel graph partitioning. In LION. Lecture Notes in Computer Science, Vol. 5851. Springer, 191-205.
[9] I. Dhillon. 2005. A fast kernel-based multilevel algorithm for graph clustering. In Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 629-634.
[10] D. Drake and S. Hougardy. 2003. A simple approximation algorithm for the weighted matching problem. Information Processing Letters 85, 211-213. · Zbl 1173.68861
[11] N. Fan and P. M. Pardalos. 2010. Linear and quadratic programming approaches for the general graph partitioning problem. Journal of Global Optimization 48, 1, 57-71. DOI: http://dx.doi.org/10.1007/s10898-009-9520-1 · Zbl 1202.90261
[12] C. M. Fiduccia and R. M. Mattheyses. 1982. A linear-time heuristic for improving network partitions. In Proceedings of the 19th Conference on Design Automation. 175-181.
[13] P. O. Fjallstrom. 1998. Algorithms for graph partitioning: A survey. Linkoping Electronic Articles in Computer and Information Science 3, 10.
[14] W. W. Hager and Y. Krylyuk. 1999. Graph partitioning and continuous quadratic programming. SIAM Journal on Discrete Mathematics 12, 4, 500-523. · Zbl 0972.90086
[15] W. W. Hager, D. T. Phan, and H. Zhang. 2013. An exact algorithm for graph partitioning. Mathematical Programming 137, 1-2, 531-556. · Zbl 1263.90115
[16] M. T. Heath. 2002. Scientific Computing: An Introductory Survey. McGraw-Hill. http://books.google.com/books?id=DPkYAQAAIAAJ. · Zbl 1411.65003
[17] M. Holtgrewe, P. Sanders, and C. Schulz. 2010. Engineering a scalable high quality graph partitioner. In Proceedings of the 24th IEEE International Symposium on Parallel and Distributed Processing. 1-10.
[18] Y. F. Hu and J. A. Scott. 2001. A multilevel algorithm for wavefront reduction. SIAM Journal on Scientific Computing 23, 4, 1352-1375. DOI: http://dx.doi.org/10.1137/S1064827500377733 · Zbl 0999.65022
[19] S. E. Karisch, F. Rendl, and J. Clausen. 2000. Solving graph bisection problems with semidefinite programming. INFORMS Journal on Computing 12, 3, 177-191. DOI: http://dx.doi.org/10.1287/ijoc.12.3. 177.12637 · Zbl 1040.90045
[20] G. Karypis and V. Kumar. 1995. Analysis of multilevel graph partitioning. In Proceedings of the 1995 ACM/IEEE Conference on Supercomputing (Supercomputing’95). Article No. 29.
[21] J. Lescovec. n.d. Stanford Network Analysis Package (SNAP). Retrieved October 20, 2014, from http://snap.stanford.edu/index.html.
[22] J. Maue and P. Sanders. 2007. Engineering algorithms for approximate weighted matching. In Experimental Algorithms. Lecture Notes in Computer Science, Vol. 4525. Springer, 242-255. http://dx.doi.org/10.1007/978-3-540-72845-0_19 · Zbl 1203.68317
[23] H. Meyerhenke, B. Monien, and T. Sauerwald. 2008. A new diffusion-based multilevel algorithm for computing graph partitions of very high quality. In Proceedings of the IEEE International Symposium on Parallel and Distributed Processing (IPDPS’08). 1-13.
[24] F. Pellegrini. Scotch Home Page. n.d. Retrieved October 20, 2014, from http://www.labri/fr/perso/pelegrin/scotch/.
[25] A. Pothen, H. D. Simon, and K.-P. Liou. 1990. Partitioning sparse matrices with eigenvectors of graphs. SIAM Journal on Matrix Analalysis and Applications 11, 3, 430-452. DOI: http://dx.doi.org/10.1137/0611030 · Zbl 0711.65034
[26] D. Ron, I. Safro, and A. Brandt. 2011. Relaxation-based coarsening and multiscale graph organization. Multiscale Modeling & Simulation 9, 1, 407-423. · Zbl 1219.68125
[27] D. Ron, S. Wishko-Stern, and A. Brandt. 2005. An Algebraic Multigrid Based Algorithm for Bisectioning General Graphs. Technical Report MCS05-01. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science.
[28] I. Safro, D. Ron, and A. Brandt. 2006. Graph minimum linear arrangement by multilevel weighted edge contractions. Journal of Algorithms 60, 1, 24-41. · Zbl 1096.68687
[29] I. Safro, D. Ron, and A. Brandt. 2008. Multilevel algorithms for linear ordering problems. Journal of Experimental Algorithmics 13, 1.4-1.20. · Zbl 1284.68685
[30] I. Safro, P. Sanders, and C. Schulz. n.d. Benchmark with Potentially Hard Graphs for Partitioning Problem. Retrieved October 20, 2014, from http://www.cs.clemson.edu/∼isafro/hardpart.html. · Zbl 1347.68355
[31] P. Sanders and C. Schulz. 2011. Engineering multilevel graph partitioning algorithms. In Algorithms—ESA 2011. Lecture Notes in Computer Science, Vol. 6942. Springer, 469-480. · Zbl 1346.05288
[32] P. Sanders and C. Schulz. 2012. Distributed evolutionary graph partitioning. In Proceedings of the 12th Workshop on Algorithm Engineering and Experimentation (ALENEX’12). 16-29. · Zbl 1430.68237
[33] K. Schloegel, G. Karypis, V. Kumar, J. Dongarra, I. Foster, G. Fox, K. Kennedy, and A. White. 2000. Graph Partitioning for High Performance Scientific Simulations. Morgan Kaufmann.
[34] E. Sharon, A. Brandt, and R. Basri. 2000. Fast multiscale image segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 70-77. citeseer.nj.nec.com/sharon99fast.html.
[35] A. J. Soper, C. Walshaw, and M. Cross. 2004. A combined evolutionary search and multilevel optimisation approach to graph-partitioning. Journal of Global Optimization 29, 2, 225-241. · Zbl 1084.90049
[36] L. E. Stock. 2006. Strategic Logistics Management. Lightning Source, La Vergne, TN. http://books.google.com/books?id=1LyCAQAACAAJ.
[37] L. Tang, H. Liu, J. Zhang, and Z. Nazeri. 2008. Community evolution in dynamic multi-mode networks. In Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’08). 677-685.
[38] U. Trottenberg and A. Schuller. 2001. Multigrid. Academic Press, Orlando, FL. · Zbl 0976.65106
[39] C. Walshaw. 2004. Multilevel refinement for combinatorial optimisation problems. Annals of Operations Research 131, 1, 325-372. · Zbl 1067.90145
[40] C. Walshaw and M. Cross. 2007. JOSTLE: Parallel multilevel graph-partitioning software—an overview. In Mesh Partitioning Techniques and Domain Decomposition Techniques, F. Magoules (Ed.). Civil-Comp Ltd., 27-58.
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