Abusing a hypergraph partitioner for unweighted graph partitioning

We investigate using the Mondriaan matrix partitioner for unweighted graph partitioning in the communication volume and edgecut metrics. By converting the unweighted graphs to appropriate matrices, we measure Mondriaan’s performance as a graph partitioner for the 10th DIMACS challenge on graph partitioning and clustering. We find that Mondriaan can effectively be used as a graph partitioner: w.r.t. the edge-cut metric, Mondriaan’s average results are within 21% of the best known results as listed in Chris Walshaw’s partitioning archive.

[1]  Rob H. Bisseling,et al.  Cache-Oblivious Sparse Matrix--Vector Multiplication by Using Sparse Matrix Partitioning Methods , 2009, SIAM J. Sci. Comput..

[2]  Bruce Hendrickson,et al.  An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations , 1995, SIAM J. Sci. Comput..

[3]  Peter Sanders,et al.  Engineering Multilevel Graph Partitioning Algorithms , 2010, ESA.

[4]  Vipin Kumar,et al.  Multilevel k-way hypergraph partitioning , 1999, DAC '99.

[5]  Timothy A. Davis,et al.  The university of Florida sparse matrix collection , 2011, TOMS.

[6]  Ümit V. Çatalyürek,et al.  Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication , 1999, IEEE Trans. Parallel Distributed Syst..

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

[8]  Vipin Kumar,et al.  Parallel Multilevel series k-Way Partitioning Scheme for Irregular Graphs , 1999, SIAM Rev..

[9]  Ümit V. Çatalyürek,et al.  Two-dimensional approaches to sparse matrix partitioning , 2012 .

[10]  William J. Knottenbelt,et al.  Parallel multilevel algorithms for hypergraph partitioning , 2008, J. Parallel Distributed Comput..

[11]  Curt Jones,et al.  A Heuristic for Reducing Fill-In in Sparse Matrix Factorization , 1993, PPSC.

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

[13]  Rob H. Bisseling,et al.  Communication balancing in parallel sparse matrix-vector multiplication , 2005 .

[14]  Ümit V. Çatalyürek,et al.  A fine-grain hypergraph model for 2D decomposition of sparse matrices , 2001, Proceedings 15th International Parallel and Distributed Processing Symposium. IPDPS 2001.

[15]  Andrew B. Kahng,et al.  Improved algorithms for hypergraph bipartitioning , 2000, ASP-DAC '00.

[16]  Chris Walshaw,et al.  A Combined Evolutionary Search and Multilevel Optimisation Approach to Graph-Partitioning , 2004, J. Glob. Optim..

[17]  Jean Roman,et al.  SCOTCH: A Software Package for Static Mapping by Dual Recursive Bipartitioning of Process and Architecture Graphs , 1996, HPCN Europe.

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

[19]  C. Walshaw JOSTLE : parallel multilevel graph-partitioning software – an overview , 2008 .

[20]  Ami Marowka,et al.  Parallel Scientific Computation: A Structured Approach using BSP and MPI , 2006, Scalable Comput. Pract. Exp..

[21]  Rob H. Bisseling,et al.  Parallel hypergraph partitioning for scientific computing , 2006, Proceedings 20th IEEE International Parallel & Distributed Processing Symposium.

[22]  Vipin Kumar,et al.  Multilevel k-way Hypergraph Partitioning , 2000, VLSI Design.

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

[24]  Vipin Kumar,et al.  Parallel Multilevel k-way Partitioning Scheme for Irregular Graphs , 1996, Proceedings of the 1996 ACM/IEEE Conference on Supercomputing.