A new diffusion-based multilevel algorithm for computing graph partitions of very high quality

IPDPS Miami 2008 - Proceedings of the 22nd IEEE International Parallel and Distributed Processing Symposium, Program and CD-ROM

Volumn , Issue , 2008, Pages

  Meyerhenke, Henning ^a   Monien, Burkhard ^a   Sauerwald, Thomas ^a  

^a UNIVERSITY OF PADERBORN   (Germany)

Author keywords

Graph partitioning; Load balancing heuristic

Indexed keywords

GRAPH PARTITIONING; LOAD BALANCING HEURISTIC;

ALGORITHMS; BENCHMARKING; BOOLEAN FUNCTIONS; COMPUTER NETWORKS; DISTRIBUTED PARAMETER NETWORKS; GRAPH THEORY; HEURISTIC PROGRAMMING; LIBRARIES; PARALLEL ALGORITHMS; SOLUTIONS; TREES (MATHEMATICS);

HEURISTIC METHODS;

EID: 51049111648     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IPDPS.2008.4536237     Document Type: Conference Paper

References (40)

1. C.-E. Bichot. A new method, the fusion fission, for the relaxed k-way graph partitioning problem, and comparisons with some multilevel algorithms. Journal of Mathematical Modelling and Algorithms, 2007. Accepted for publication: 1st December 2006, published online: 16th March 2007.
2. U. Catalyurek, E. Boman, K. Devine, D. Bozdag, R. Heaphy, and L. Riesen. Hypergraph-based dynamic load balancing for adaptive scientific computations. In Proc. 21st Intl. Parallel and Distributed Processing Symposium (IPDPS'07). IEEE, 2007.
3. C. Chevalier and F. Pellegrini. Improvement of the efficiency of genetic algorithms for scalable parallel graph partitioning in a multi-level framework. In Proc. Intl. Euro-Par Conf. (Euro-Par'06), volume 4128 of LNCS, pages 243-252. Springer, 2006.
4. G. Cybenko. Dynamic load balancing for distributed memory multiprocessors. Parallel and Distributed Computing, 7:279-301, 1989.
5. M. Dellnitz, M. Hessel-von Molo, P. Metzner, R. Preis, and C. Schütte. Graph algorithms for dynamical systems. In Modeling and Simulation of Multiscale Problems, pages 619-646. Springer, 2006.
6. K. Devine, E. Boman, R. Heaphy, R. Bisseling, and U. Catalyurek. Parallel hypergraph partitioning for scientific computing. In Proc. 20th Intl. Parallel and Distributed Processing Symposium (IPDPS'06). IEEE, 2006.
7. R. Diekmann, R. Preis, F. Schlimbach, and C. Walshaw. Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM. J. Parallel Computing, 26:1555-1581, 2000.
8. R. Elsässer, B. Monien, and R. Preis. Diffusion schemes for load balancing on heterogeneous networks. Theory of Computing Systems, 35:305-320, 2002.
9. C. M. Fiduccia and R. M. Mattheyses. A linear-time heuristic for improving network partitions. In Proc. 19th conference on Design automation (DAC'82), pages 175-181. IEEE Press, 1982.
10. D. Harel and Y. Koren. On clustering using random walks. In Proc. 21st Foundations of Software Technology and Theoretical Computer Science (FSTTCS'01), volume 2245 of LNCS, pages 18-41. Springer, 2001.
11. B. Hendrickson. Graph partitioning and parallel solvers: Has the emperor no clothes? In Proc. Irregular'98, volume 1457 of LNCS, pages 218-225. Springer, 1998.
12. B. Hendrickson and R. Leland. An improved spectral graph partitioning algorithm for mapping parallel computations. SIAM J. Sci. Comput., 16(2):452-469, 1995.
13. B. Hendrickson and R. Leland. A multi-level algorithm for partitioning graphs. In Proc. ACM/IEEE Conf. Supercomputing (CDROM), page 28, 1995.
14. S. Huang, E. Aubanel, and V. C. Bhavsar. PaGrid: A mesh partitioner for computational grids. J. Grid Comput., 4(1):71-88, 2006.
15. G. Karypis and V. Kumar. MeTiS: A Software Package for Partitioning Unstrctured Graphs, Partitioning Meshes, [...], Version 4.0, 1998.
16. G. Karypis and V. Kumar. Multilevel k-way partitioning scheme for irregular graphs. J. Parallel Distrib. Comput., 48(1):96-129, 1998.
17. B. W. Kernighan and S. Lin. An efficient heuristic for partitioning graphs. Bell Systems Technical Journal, 49:291-308, 1970.
18. R. Khandekar, S. Rao, and U. Vazirani. Graph partitioning using single commodity flows. In Proc. 38th Symp. on Theory of Computing (STOC'06), pages 385-390. ACM, 2006.
19. S. P. Lloyd. Least squares quantization in PCM. IEEE Trans. on Information Theory, 28(2):129-136, 1982.
20. H. Meyerhenke. Graph partitioning for balancing parallel adaptive numerical simulations. http://wwwcs.upb.de/cs/henningm/graph.html, 2007.
21. H. Meyerhenke, B. Monien, and S. Schamberger. Accelerating shape optimizing load balancing for parallel FEM simulations by algebraic multigrid. In Proc. 20th Intl. Parallel and Distributed Processing Symposium (IPDPS'06). IEEE, 2006.
22. H. Meyerhenke and T. Sauerwald. Analyzing disturbed diffusion on networks. In Proc. 17th International Symposium on Algorithms and Computation (ISAAC'06), volume 4288 of LNCS, pages 429-438. Springer, 2006.
23. H. Meyerhenke and S. Schamberger. Balancing parallel adaptive FEM computations by solving systems of linear equations. In Proc. 11th Intl. Euro-Par Conf. (Euro-Par'05), volume 3648 of LNCS, pages 209-219, 2005.
24. H. Meyerhenke and S. Schamberger. A parallel shape optimizing load balancer. In Proc. 12th Intl. Euro-Par Conf. (Euro-Par'06), volume 4128 of LNCS, pages 232-242, 2006.
25. F. Pellegrini. A parallelisbale multi-level banded diffusion scheme for computing balanced partitions with smooth boundaries. In 13th Proc. Intl. Euro-Par Conf. (Euro-Par'07), volume 4641 of LNCS, pages 195-204. Springer, 2007.
26. F. Pellegrini. Scotch and libscotch 5.0 user's guide. Technical report, LaBRI, Université Bordeaux I, December 2007.
27. R. Preis. Linear time 1/2-approximation algorithm for maximum weighted matching in general graphs. In Proc. 16th Symp. on Theoretical Aspects of Computer Science (STACS'99), volume 1563 of LNCS, pages 259-269, 1999.
28. S. Schamberger. On partitioning FEM graphs using diffusion. In Proc. HPGC Workshop of 18th Intern. Parallel and Distributed Processing Symposium (IPDPS'04), 2004.
29. S. Schamberger. Shape Optimized Graph Partitioning. PhD thesis, Universität Paderborn, 2006.
30. K. Schloegel, G. Karypis, and V. Kumar. Parallel static and dynamic multi-constraint graph partitioning. Concurrency and Computation: Practice and Experience, 14(3):219-240, 2002.
31. K. Schloegel, G. Karypis, and V. Kumar. Graph partitioning for high performance scientific simulations. In The Sourcebook of Parallel Computing, pages 491-541. Morgan Kaufmann, 2003.
32. J. Shi and J. Malik. Normalized cuts and image segmentation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 22(8):888-905, 2000.
33. A. J. Soper, C. Walshaw, and M. Cross. A combined evolutionary search and multilevel optimisation approach to graph partitioning. J. Global Optimization, 29(2):225-241, 2004.
34. D. A. Spielman and S.-H. Teng. Spectral partitioning works: Planar graphs and finite element meshes. In Proc. 37th Symp. on Foundations of Computer Science (FOCS'96), pages 96-105. IEEE, 1996.
35. K. Stüben. An introduction to algebraic multigrid. In U. Trottenberg, C. W. Oosterlee, and A. Schüller, editors, Multigrid, pages 413-532. Academic Press, London, 2000. Appendix A.
36. U. Trottenberg, C.W. Oosterlee, and A. Schüller. Multigrid. Academic Press, 2000.
37. C. Walshaw. The graph partitioning archive. http://staffweb.cms.gre.ac. uk/~c.walshaw/partition/, 2007.
38. C. Walshaw and M. Cross. Mesh partitioning: a multilevel balancing and refinement algorithm. SIAM J. Sci. Comput., 22(1):63-80, 2000.
39. C. Walshaw and M. Cross. Parallel optimisation algorithms for multilevel mesh partitioning. J. Parallel Computing, 26(12):1635-1660, 2000.
40. G. Zumbusch. Parallel Multilevel Methods: Adaptive Mesh Refinement and Loadbalancing. Teubner, 2003.