Mapping Affine Loop Nests: Solving of the Alignment and Scheduling Problems

The paper is devoted to the problem of mapping affine loop nests onto distributed memory parallel computers. An algorithm to find an efficient scheduling and distribution of data and operations to virtual processors is presented. It reduces the sheduling and the alignment problems to the solving of linear algebraic equations. The algorithm finds the maximal degree of pipelined parallelism and tries to minimize the number of nonlocal communications.