On Grid-based Matrix Partitioning for Heterogeneous Processors

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(p^3/2) solving this problem is proposed, proved and experimentally validated.