Graph Partitioning, Ordering, and Clustering for Multicore Architectures

University of Minnesota Ph.D. dissertation. December 2015. Major: Computer Science. Advisor: George Karypis. 1 computer file (PDF); xiii, 154 pages.

[1]  H. Markowitz The Elimination form of the Inverse and its Application to Linear Programming , 1957 .

[2]  Ilya Safro,et al.  Multilevel algorithms for linear ordering problems , 2009, JEAL.

[3]  P Cignoni,et al.  DeWall: A fast divide and conquer Delaunay triangulation algorithm in Ed , 1998, Comput. Aided Des..

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

[5]  Sivasankaran Rajamanickam,et al.  Parallel partitioning with Zoltan: Is hypergraph partitioning worth it? , 2012, Graph Partitioning and Graph Clustering.

[6]  Harold N. Gabow,et al.  Data structures for weighted matching and nearest common ancestors with linking , 1990, SODA '90.

[7]  A. Hoffman,et al.  Lower bounds for the partitioning of graphs , 1973 .

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

[9]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

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

[11]  Richard McDougall,et al.  Solaris Internals: Solaris 10 and OpenSolaris Kernel Architecture , 2006 .

[12]  David A. Bader,et al.  Scalable Multi-threaded Community Detection in Social Networks , 2012, 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum.

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

[14]  S H Strogatz,et al.  Random graph models of social networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Joseph W. H. Liu,et al.  Modification of the minimum-degree algorithm by multiple elimination , 1985, TOMS.

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

[17]  E. N. Gilbert,et al.  Random Plane Networks , 1961 .

[18]  Dorothea Wagner,et al.  Engineering multilevel overlay graphs for shortest-path queries , 2009, JEAL.

[19]  Shashi Shekhar,et al.  Multilevel hypergraph partitioning: application in VLSI domain , 1997, DAC.

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

[21]  S. Lakshminarayana,et al.  Categorization of web pages - Performance enhancement to search engine , 2009, Knowl. Based Syst..

[22]  R. Bisseling,et al.  DNA Electrophoresis Studied with the Cage Model , 2001, cond-mat/0101467.

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

[24]  William W. Hager,et al.  Continuous quadratic programming formulations of optimization problems on graphs , 2015, Eur. J. Oper. Res..

[25]  Peter Sanders,et al.  Distributed Evolutionary Graph Partitioning , 2011, ALENEX.

[26]  D. Calvetti,et al.  AN IMPLICITLY RESTARTED LANCZOS METHOD FOR LARGE SYMMETRIC EIGENVALUE PROBLEMS , 1994 .

[27]  Fabrizio Silvestri,et al.  Know your neighbors: web spam detection using the web topology , 2007, SIGIR.

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

[29]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[30]  François Pellegrini,et al.  PT-Scotch and libScotch 5.1 User's Guide , 2007 .

[31]  Sebastiano Vigna,et al.  UbiCrawler: a scalable fully distributed Web crawler , 2004, Softw. Pract. Exp..

[32]  Curt Jones,et al.  Finding Good Approximate Vertex and Edge Partitions is NP-Hard , 1992, Inf. Process. Lett..

[33]  John K. Reid,et al.  Exploiting zeros on the diagonal in the direct solution of indefinite sparse symmetric linear systems , 1996, TOMS.

[34]  Ralf Diekmann,et al.  Quality matching and local improvement for multilevel graph-partitioning , 2000, Parallel Comput..

[35]  C. Kuratowski Sur le problème des courbes gauches en Topologie , 1930 .

[36]  Horst D. Simon,et al.  Partitioning of unstructured problems for parallel processing , 1991 .

[37]  Vipin Kumar,et al.  A Parallel Algorithm for Multilevel Graph Partitioning and Sparse Matrix Ordering , 1998, J. Parallel Distributed Comput..

[38]  A. Arenas,et al.  Community detection in complex networks using extremal optimization. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Vipin Kumar,et al.  Analysis of Multilevel Graph Partitioning , 1995, Proceedings of the IEEE/ACM SC95 Conference.

[40]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[41]  Jon M. Kleinberg,et al.  Group formation in large social networks: membership, growth, and evolution , 2006, KDD '06.

[42]  Andreas Geyer-Schulz,et al.  An ensemble learning strategy for graph clustering , 2012, Graph Partitioning and Graph Clustering.

[43]  George Karypis,et al.  Multi-threaded modularity based graph clustering using the multilevel paradigm , 2015, J. Parallel Distributed Comput..

[44]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[45]  A. Lamecki,et al.  Tuning a Hybrid GPU-CPU V-Cycle Multilevel Preconditioner for Solving Large Real and Complex Systems of FEM Equations , 2011, IEEE Antennas and Wireless Propagation Letters.

[46]  Alan George,et al.  Communication results for parallel sparse Cholesky factorization on a hypercube , 1989, Parallel Comput..

[47]  George Karypis,et al.  Multi-threaded Graph Partitioning , 2013, 2013 IEEE 27th International Symposium on Parallel and Distributed Processing.

[48]  Robert L. Scot Drysdale,et al.  A comparison of sequential Delaunay triangulation algorithms , 1995, SCG '95.

[49]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  Shantanu Dutt,et al.  VLSI circuit partitioning by cluster-removal using iterative improvement techniques , 1996, ICCAD 1996.

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

[52]  Johnson M. Hart,et al.  Windows System Programming , 2004 .

[53]  Huan Liu,et al.  Community Detection and Mining in Social Media , 2010, Community Detection and Mining in Social Media.

[54]  Shashi Shekhar,et al.  Partitioning Similarity Graphs: A Framework for Declustering Problems , 1996, Inf. Syst..

[55]  Enrique S. Quintana-Ortí,et al.  Evaluation of Parallel Sparse Matrix Partitioning Software for Parallel Multilevel ILU Preconditioning on Shared-Memory Multiprocessors , 2009, PARCO.

[56]  Michael T. Heath,et al.  Sparse Cholesky factorization on a local-memory multiprocessor , 1988 .

[57]  George Karypis,et al.  Multilevel k-way Partitioning Scheme for Irregular Graphs , 1998, J. Parallel Distributed Comput..

[58]  S. Fortunato,et al.  Resolution limit in community detection , 2006, Proceedings of the National Academy of Sciences.

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

[60]  Ulrik Brandes,et al.  On Modularity Clustering , 2008, IEEE Transactions on Knowledge and Data Engineering.

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

[62]  Christian Staudt,et al.  Engineering High-Performance Community Detection Heuristics for Massive Graphs , 2013, 2013 42nd International Conference on Parallel Processing.

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

[64]  Andreas Noack,et al.  Multi-level Algorithms for Modularity Clustering , 2008, SEA.

[65]  Timothy A. Davis,et al.  Direct methods for sparse linear systems , 2006, Fundamentals of algorithms.

[66]  L. Takac DATA ANALYSIS IN PUBLIC SOCIAL NETWORKS , 2012 .

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

[68]  Andrew V. Goldberg,et al.  An exact combinatorial algorithm for minimum graph bisection , 2014, Math. Program..

[69]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  M. Fiedler Algebraic connectivity of graphs , 1973 .

[71]  Peter Sanders,et al.  In Transit to Constant Time Shortest-Path Queries in Road Networks , 2007, ALENEX.

[72]  Alex Pothen,et al.  PARTITIONING SPARSE MATRICES WITH EIGENVECTORS OF GRAPHS* , 1990 .

[73]  Inderjit S. Dhillon,et al.  Scalable and Memory-Efficient Clustering of Large-Scale Social Networks , 2012, 2012 IEEE 12th International Conference on Data Mining.

[74]  Oliver Marquardt,et al.  Open Benchmarks for Load Balancing Heuristics in Parallel Adaptive Finite Element Computations , 2005, PDPTA.

[75]  Rob H. Bisseling,et al.  Graph coarsening and clustering on the GPU , 2012, Graph Partitioning and Graph Clustering.

[76]  P. J. Narayanan,et al.  Accelerating Large Graph Algorithms on the GPU Using CUDA , 2007, HiPC.

[77]  H. Simon,et al.  ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS , 1955 .

[78]  Olaf Schenk,et al.  Inertia-Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization , 2008, SIAM J. Sci. Comput..

[79]  Pinar Heggernes,et al.  The Computational Complexity of the Minimum Degree Algorithm , 2001 .

[80]  Andrew B. Kahng,et al.  Recent directions in netlist partitioning: a survey , 1995, Integr..

[81]  Miao Xu,et al.  Speedup Matrix Completion with Side Information: Application to Multi-Label Learning , 2013, NIPS.