Current challenges in parallel graph partitioning

Graph partitioning is a technique used for the solving of many problems in scientific computing, such as the decomposition of a mesh into domains so as to evenly balance the compute load on the processors of a parallel architecture. Because of the ever increasing size of the meshes to handle, partitioning tools themselves had to be parallelized. The parallel versions of these software provide good results for and on several thousands of processors, but the advent of architectures comprising more than a million processing elements raises new problems. Not only do the partitioning results produced by these software have to take into account the heterogeneity of these architectures, but also does the efficient execution of the partitioning software on these architectures require much more sophisticated algorithms. The purpose of this talk is to present the challenges to overcome in order to reach these goals.

[1]  Charbel Farhat,et al.  A simple and efficient automatic fem domain decomposer , 1988 .

[2]  Bruce Hendrickson,et al.  Improving the Run Time and Quality of Nested Dissection Ordering , 1998, SIAM J. Sci. Comput..

[3]  Brendan Vastenhouw,et al.  A Two-Dimensional Data Distribution Method for Parallel Sparse Matrix-Vector Multiplication , 2005, SIAM Rev..

[4]  Brian W. Kernighan,et al.  An efficient heuristic procedure for partitioning graphs , 1970, Bell Syst. Tech. J..

[5]  Roberto Battiti,et al.  Greedy, Prohibition, and Reactive Heuristics for Graph Partitioning , 1999, IEEE Trans. Computers.

[6]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[7]  Bruce Hendrickson,et al.  A Multi-Level Algorithm For Partitioning Graphs , 1995, Proceedings of the IEEE/ACM SC95 Conference.

[8]  R. M. Mattheyses,et al.  A Linear-Time Heuristic for Improving Network Partitions , 1982, 19th Design Automation Conference.

[9]  François Pellegrini,et al.  PT-Scotch: A tool for efficient parallel graph ordering , 2008, Parallel Comput..

[10]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[11]  Byung Ro Moon,et al.  Genetic Algorithm and Graph Partitioning , 1996, IEEE Trans. Computers.

[12]  Scott F. Midkiff,et al.  Processor and Link Assignment in Multicomputers Using Simulated Annealing , 1988, ICPP.

[13]  B. Nour-Omid,et al.  Solving finite element equations on concurrent computers , 1987 .

[14]  Martin G. Everett,et al.  Partitioning & Mapping of Unstructured Meshes to Parallel Machine Topologies , 1995, IRREGULAR.

[15]  Horst D. Simon,et al.  Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems , 1994, Concurr. Pract. Exp..

[16]  François Pellegrini,et al.  A Parallelisable Multi-level Banded Diffusion Scheme for Computing Balanced Partitions with Smooth Boundaries , 2007, Euro-Par.

[17]  F. Pellegrini,et al.  Static mapping by dual recursive bipartitioning of process architecture graphs , 1994, Proceedings of IEEE Scalable High Performance Computing Conference.

[18]  Manuel Laguna,et al.  A Greedy Randomized Adaptive Search Procedure for the Two-Partition Problem , 1994, Oper. Res..

[19]  Vipin Kumar,et al.  Multilevel Graph Partitioning Schemes , 1995, ICPP.

[20]  Ralf Diekmann,et al.  Aspect Radio for Mesh Partitioning , 1998, Euro-Par.

[21]  François Pellegrini,et al.  Improvement of the Efficiency of Genetic Algorithms for Scalable Parallel Graph Partitioning in a Multi-level Framework , 2006, Euro-Par.

[22]  P. W. Grant,et al.  Using Competing Ant Colonies to Solve k-way Partitioning Problems with Foraging and Raiding Strategies , 1999, ECAL.

[23]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .