A scalable hybrid linear solver based on combinatorial algorithms

[1]  Rob H. Bisseling,et al.  A Parallel Approximation Algorithm for the Weighted Maximum Matching Problem , 2007, PPAM.

[2]  James Demmel,et al.  CALU: A Communication Optimal LU Factorization Algorithm , 2011, SIAM J. Matrix Anal. Appl..

[3]  Robert Preis,et al.  Linear Time 1/2-Approximation Algorithm for Maximum Weighted Matching in General Graphs , 1999, STACS.

[4]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[5]  J. M. Wein,et al.  Massively parallel auction algorithms for the assignment problem , 1990, [1990 Proceedings] The Third Symposium on the Frontiers of Massively Parallel Computation.

[6]  E. Cuthill,et al.  Reducing the bandwidth of sparse symmetric matrices , 1969, ACM '69.

[7]  James Demmel,et al.  Making Sparse Gaussian Elimination Scalable by Static Pivoting , 1998, Proceedings of the IEEE/ACM SC98 Conference.

[8]  David A. Bader,et al.  Parallel Shortest Path Algorithms for Solving Large-Scale Instances , 2006, The Shortest Path Problem.

[9]  J. A. George Computer implementation of the finite element method , 1971 .

[10]  Murat Manguoglu,et al.  Parallel scalable PDE-constrained optimization: antenna identification in hyperthermia cancer treatment planning , 2009, Computer Science - Research and Development.

[11]  Murat Manguoglu,et al.  Weighted Matrix Ordering and Parallel Banded Preconditioners for Iterative Linear System Solvers , 2010, SIAM J. Sci. Comput..

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

[13]  David Avis,et al.  A survey of heuristics for the weighted matching problem , 1983, Networks.

[14]  Shahid H. Bokhari,et al.  Partitioning Problems in Parallel, Pipelined, and Distributed Computing , 1988, IEEE Trans. Computers.

[15]  M. Patwary,et al.  Parallel greedy graph matching using an edge partitioning approach , 2010, HLPP '10.

[16]  Berkant Barla Cambazoglu,et al.  Multi-level direct K-way hypergraph partitioning with multiple constraints and fixed vertices , 2008, J. Parallel Distributed Comput..

[17]  Jörg Peters,et al.  The network simplex method on a multiprocessor , 1990, Networks.

[18]  Michael W. Berry,et al.  Multiprocessor Schemes for Solving Block Tridiagonal Linear Systems , 1988 .

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

[20]  Shang-Hua Teng,et al.  How Good is Recursive Bisection? , 1997, SIAM J. Sci. Comput..

[21]  Pavel Tvrdík,et al.  Towards auction algorithms for large dense assignment problems , 2009, Comput. Optim. Appl..

[22]  Hisao Tamaki,et al.  Greedily Finding a Dense Subgraph , 2000, J. Algorithms.

[23]  Cevdet Aykanat,et al.  One-dimensional partitioning for heterogeneous systems: Theory and practice , 2008, J. Parallel Distributed Comput..

[24]  A. Neumaier,et al.  A NEW PIVOTING STRATEGY FOR GAUSSIAN ELIMINATION , 1996 .

[25]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[26]  Ahmed Sameh,et al.  Hybrid Parallel Linear System Solvers , 1999 .

[27]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[28]  Ahmed Sameh,et al.  SPIKE: A parallel environment for solving banded linear systems , 2007 .

[29]  Mauro Dell'Amico,et al.  Assignment Problems , 1998, IFIP Congress: Fundamentals - Foundations of Computer Science.

[30]  H. D. Simon,et al.  A spectral algorithm for envelope reduction of sparse matrices , 1993, Supercomputing '93. Proceedings.

[31]  Olaf Schenk,et al.  An Interior-Point Algorithm for Large-Scale Nonlinear Optimization with Inexact Step Computations , 2010, SIAM J. Sci. Comput..

[32]  Murat Manguoglu,et al.  Analysis of the Truncated SPIKE Algorithm , 2008, SIAM J. Matrix Anal. Appl..

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

[34]  Jack J. Dongarra,et al.  On some parallel banded system solvers , 1984, Parallel Comput..

[35]  Yves Robert,et al.  Mapping pipeline skeletons onto heterogeneous platforms , 2007, J. Parallel Distributed Comput..

[36]  H. Kuhn The Hungarian method for the assignment problem , 1955 .

[37]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .

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

[39]  Olaf Schenk,et al.  Weighted Matchings for Preconditioning Symmetric Indefinite Linear Systems , 2006, SIAM J. Sci. Comput..

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

[41]  Olaf Schenk,et al.  Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization , 2007, Comput. Optim. Appl..

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

[43]  Seid Koric,et al.  Sparse matrix factorization on massively parallel computers , 2009, Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis.

[44]  David J. Kuck,et al.  Practical Parallel Band Triangular System Solvers , 1978, TOMS.

[45]  A. Pothen,et al.  Two improved algorithms for envelope and wavefront reduction , 1997 .

[46]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[47]  Bojan Mohar,et al.  Optimal linear labelings and eigenvalues of graphs , 1992, Discret. Appl. Math..

[48]  Ahmed H. Sameh,et al.  A parallel hybrid banded system solver: the SPIKE algorithm , 2006, Parallel Comput..

[49]  David Pisinger,et al.  The quadratic knapsack problem - a survey , 2007, Discret. Appl. Math..

[50]  John Reid,et al.  Ordering symmetric sparse matrices for small profile and wavefront , 1999 .

[51]  Duncan H. Lawrie,et al.  The computation and communication complexity of a parallel banded system solver , 1984, TOMS.

[52]  David J. Kuck,et al.  On Stable Parallel Linear System Solvers , 1978, JACM.

[53]  Peter Sanders,et al.  Heuristic initialization for bipartite matching problems , 2010, JEAL.

[54]  Dimitri P. Bertsekas,et al.  Parallel synchronous and asynchronous implementations of the auction algorithm , 1991, Parallel Comput..

[55]  Helmut Maurer,et al.  Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints: Part 1. Boundary Control , 2000, Comput. Optim. Appl..

[56]  Donald L. Miller,et al.  Solution of large dense transportation problems using a parallel primal algorithm , 1990 .

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

[58]  S. Sloan An algorithm for profile and wavefront reduction of sparse matrices , 1986 .

[59]  George Karypis,et al.  Multilevel Hypergraph Partitioning , 2003 .

[60]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[61]  Stefan Hougardy,et al.  Approximating weighted matchings in parallel , 2006, Inf. Process. Lett..

[62]  M. Fiedler A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory , 1975 .

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

[64]  A. Sameh,et al.  A tearing-based hybrid parallel banded linear system solver , 2009 .

[65]  Cevdet Aykanat,et al.  Fast optimal load balancing algorithms for 1D partitioning , 2004, J. Parallel Distributed Comput..

[66]  Alan George,et al.  An Implementation of a Pseudoperipheral Node Finder , 1979, TOMS.

[67]  Bruce Hendrickson,et al.  The Chaco user`s guide. Version 1.0 , 1993 .

[68]  I. Duff,et al.  THE USE OF PROFILE REDUCTION ALGORITHMS WITH A FRONTAL CODE , 1989 .

[69]  O. Schenk,et al.  ON FAST FACTORIZATION PIVOTING METHODS FOR SPARSE SYMMETRI C INDEFINITE SYSTEMS , 2006 .

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

[71]  Iain S. Duff,et al.  On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix , 2000, SIAM J. Matrix Anal. Appl..

[72]  Ran Duan,et al.  Approximating Maximum Weight Matching in Near-Linear Time , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[73]  Michael Luby A Simple Parallel Algorithm for the Maximal Independent Set Problem , 1986, SIAM J. Comput..

[74]  Jennifer A. Scott,et al.  A Multilevel Algorithm for Wavefront Reduction , 2001, SIAM J. Sci. Comput..

[75]  Murat Manguoglu,et al.  TRACEMIN-Fiedler: A Parallel Algorithm for Computing the Fiedler Vector , 2010, VECPAR.

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

[77]  Milind Dawande,et al.  On Bipartite and Multipartite Clique Problems , 2001, J. Algorithms.

[78]  Murat Manguoglu,et al.  PSPIKE: A Parallel Hybrid Sparse Linear System Solver , 2009, Euro-Par.