Adaptive-blocking hierarchical storage format for sparse matrices

Hierarchical storage formats (HSFs) can significantly reduce the space complexity of sparse matrices. They vary in storage schemes that they use for blocks and for block matrices. However, the current HSFs prescribe a fixed storage scheme for all blocks, which is not always space-optimal. We show that, generally, different storage schemes are space-optimal for different blocks. We further propose a new HSF that is based on this approach and compare its space complexity with current HSFs for benchmark matrices arising from different application areas.

[1]  Pavel Tvrdík,et al.  Space-efficient Sparse Matrix Storage Formats for Massively Parallel Systems , 2012, 2012 IEEE 14th International Conference on High Performance Computing and Communication & 2012 IEEE 9th International Conference on Embedded Software and Systems.

[2]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[3]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

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

[5]  James Demmel,et al.  Performance Optimizations and Bounds for Sparse Matrix-Vector Multiply , 2002, ACM/IEEE SC 2002 Conference (SC'02).

[6]  Stamatis Vassiliadis,et al.  A Hierarchical sparse matrix storage format for vector processors , 2003, Proceedings International Parallel and Distributed Processing Symposium.

[7]  John R. Gilbert,et al.  Parallel sparse matrix-vector and matrix-transpose-vector multiplication using compressed sparse blocks , 2009, SPAA '09.

[8]  Pavel Tvrdík,et al.  Sparse Matrix-Vector Multiplication - Final Solution? , 2007, PPAM.

[9]  Pyrros Theofanis Stathis.  Sparse Matrix Vector Processing Formats , 2004 .

[10]  Daniel Langr,et al.  Adaptive-Blocking Hierarchical Storage Format for , 2012 .

[11]  Stamatis Vassiliadis,et al.  Sparse Matrix Storage Format , 2005 .

[12]  Daniel Langr,et al.  Symmetry-adapted Ab Initio Theory for Many-body Correlations in Nuclei , 2011 .

[13]  Marcin Paprzycki,et al.  Use of hybrid recursive CSR/COO data structures in sparse matrix-vector multiplication , 2010, Proceedings of the International Multiconference on Computer Science and Information Technology.

[14]  Marcin Paprzycki,et al.  On the Usage of 16 Bit Indices in Recursively Stored Sparse Matrices , 2010, 2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing.

[15]  Anila Usman,et al.  Blocked-based sparse matrix-vector multiplication on distributed memory parallel computers , 2011, Int. Arab J. Inf. Technol..