Cache-aware matrix multiplication on multicore systems for IPM-based LP solvers

Author

Eleyat, Mujahed ; Natvig, Lasse ; Amundsen, Jørn

Author_Institution

Miriam AS, NTNU, Trondheim, Norway

fYear

2011

fDate

18-21 Sept. 2011

Firstpage

431

Lastpage

438

Abstract

We profile GLPK, an open source linear programming solver, and show empirically that the form of matrix multiplication used in interior point methods takes a significant portion of the total execution time when solving some of the Netlib and other LP data sets. Then, we discuss the drawbacks of the matrix multiplication algorithm used in GLPK in terms of cache utilization and use blocking to develop two cache-aware implementations. We apply OpenMP to develop parallel implementations with load balancing. The best implementation achieved a median speedup of 21.9 when executed on a 12-core AMD Opteron.

Keywords

application program interfaces; cache storage; digital arithmetic; linear programming; matrix multiplication; multiprocessing systems; resource allocation; 12-core AMD Opteron; GLPK; IPM-based LP solvers; Netlib; OpenMP; cache utilization; cache-aware matrix multiplication; interior point methods; load balancing; multicore systems; open source linear programming solver; Arrays; Multicore processing; Partitioning algorithms; Program processors; Sparse matrices; Symmetric matrices; Vectors; cache optimization; interior point methods; multicore systems; sparse matrix multiplication;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Science and Information Systems (FedCSIS), 2011 Federated Conference on

Conference_Location

Szczecin

Print_ISBN

978-1-4577-0041-5

Electronic_ISBN

978-83-60810-35-4

Type

conf

Filename

6078258