Title :
On Grid-based Matrix Partitioning for Heterogeneous Processors
Author :
Lastovetsky, Alexey
Author_Institution :
Univ. Coll. Dublin, Dublin
Abstract :
The problem of optimal matrix partitioning for parallel linear algebra on p heterogeneous processors is typically reduced to the geometrical problem of partitioning a unit square into rectangles. In the most general case, the problem has proved NP-complete. Therefore, restrictions of this problem allowing for polynomial solutions should be studied. So far, the only well-studied restriction has been a column-based geometrical partitioning problem obtained from the general problem by imposing the additional restriction that rectangles of the partitioning make up columns. This problem has a solution of the complexity O(p3) . This paper studies another restriction - a grid-based partitioning problem obtained from the general problem by imposing the additional restriction that the heterogeneous processors owing the rectangles of the partitioning form a two-dimensional grid. An algorithm of the complexity O(p3/2) solving this problem is proposed, proved and experimentally validated.
Keywords :
computational complexity; geometry; grid computing; mathematics computing; matrix algebra; parallel processing; NP-complete problem; algorithm complexity; column-based geometrical partitioning problem; grid-based optimal matrix partitioning problem; heterogeneous processor; parallel linear algebra; Algorithm design and analysis; Computer networks; Concurrent computing; Distributed computing; Linear algebra; Parallel algorithms; Parallel architectures; Partitioning algorithms; Polynomials; Workstations;
Conference_Titel :
Parallel and Distributed Computing, 2007. ISPDC '07. Sixth International Symposium on
Conference_Location :
Hagenberg
DOI :
10.1109/ISPDC.2007.38